Imaginesis: printable Year 6 Addition, Subtraction, Multiplication and Division maths worksheets for England (National Curriculum) — Finding the Least Common Multiple, Finding the Greatest Common Factor, Solving Two-Step Word Problems: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
Alex empties a mechanical leaf sweeper along the turf lane every 3 days, and Nora empties a second sweeper along the parallel lane every 11 days. Both sweepers are emptied today. After how many days will both sweepers next be emptied on the same day?
Hint: List the days when Alex empties a sweeper and the days when Nora empties a sweeper. Look for the smallest number of days that appears on both lists.
Answer: 33
At an animal shelter, 20 dog biscuits and 55 chew toys are to be packed into identical gift bags for new owners. Every bag gets the same number of biscuits and the same number of toys, and nothing is left over. What is the greatest number of gift bags that can be made?
Hint: Try a number of bags and check whether both the biscuits and the toys share out with nothing left over.
Answer: 5
The prep table holds 22 bowls of chopped carrots. Another 16 bowls of chopped carrots were brought from the fridge, and 24 more bowls were filled from the counter. How many bowls of chopped carrots are on the prep table in all?
Hint: First, add the 22 bowls of chopped carrots to the 16 bowls from the fridge, and then add the last 24 bowls.
Answer: 62
Children learn to find the smallest common multiple of given numbers and use it to solve practical problems about repeating events.
KS3.N.3 use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation propertyY6.ASMD.5 identify common factors, common multiples and prime numbers
In Year 6, children learn to identify common multiples of numbers and pinpoint the least common multiple (LCM). They work systematically by comparing the times-table multiples of two or more given numbers to determine the lowest number that appears in both lists.
A frequent stumbling block is confusing multiples with factors, leading children to search for smaller divisors rather than larger products. Another common error is simply multiplying the two numbers together; while this always produces a common multiple, it often misses the least common multiple (such as giving 24 instead of 12 for the numbers 4 and 6).
In class, this skill appears in direct calculation tasks such as Find the least common multiple, where children practice with number pairs. They also apply the skill to real-world word problems in When together again?, calculating when repeating cycles—such as two buses on different timetables or two flashing signals—will happen at the same time.
Children learn to identify the common factors of whole numbers and determine the largest shared factor to solve division and sharing problems.
KS3.N.3 use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation propertyY5.MD.1 identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbersY6.ASMD.5 identify common factors, common multiples and prime numbers
In Year 6, children build on their knowledge of multiplication tables to find common factors between two whole numbers. Pupils systematically list factor pairs for each number and compare them to identify the greatest common factor—the largest whole number that divides into both without leaving a remainder.
A frequent stumbling block is confusing factors with multiples, leading children to list larger numbers produced by multiplication rather than smaller divisors. Pupils also commonly settle on the first common factor they notice—often 2 when working with even numbers—rather than checking all factor pairs to ensure they have found the largest one.
Worksheet tasks typically present this skill in two formats:
Children learn to break down and solve real-world word problems that require two calculation steps to combine quantities and reach a final total.
Y3.AS.4 solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.Y4.AS.3 solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.Y4.NPV.8 solve number and practical problems that involve all of the above and with increasingly large positive numbersY5.AS.4 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.Y5.NPV.5 solve number problems and practical problems that involve all of the aboveY6.ASMD.7 solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and whyY6.ASMD.8 solve problems involving addition, subtraction, multiplication and divisionY6.NPV.4 solve number and practical problems that involve all of the above.
Children tackle practical contexts where they must decide which operations and methods to use and why. At this stage, they work with increasingly large positive numbers, identifying the intermediate result needed before completing the final step using addition and subtraction.
A frequent error occurs when pupils stop after completing only the first calculation. Because word problems often present information sequentially, children easily mistake the intermediate answer for the final solution, or they latch onto individual keywords rather than working out how the different quantities combine across both steps.
Worksheet tasks use the two-step word problem (combine) template. A typical question describes a real-life situation—such as calculating items collected across different groups or dates—requiring children to carry out an initial addition or subtraction, store that total, and combine it in a second step to find the overall answer.
