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      Lesson details

      Learning outcome

      I can use the prime factorisation of two or more positive integers to efficiently find their lowest common multiple.

      Key learning points

      1. Common multiples can be found using the prime factorisation of numbers
      2. The lowest common multiple of two numbers can be found by comparing the prime factorisation of both numbers
      3. Sometimes a Venn diagram can help identify the lowest common multiple of two numbers
      4. The lowest common multiple of more than two numbers can be found using prime factorisation

      Keywords

      • Lowest common multiple - The lowest common multiple is the lowest number that is a multiple of two or more integers.

      • LCM - LCM is an abbreviation for lowest common multiple.

      Common misconception

      When using a Venn diagram misplacement of factors is common.

      Encourage students to check that the product of factors in each set is the correct integer.

      Teacher tip

      Before going through writing multiples of integers given in prime factor form get the students to try doing this themselves on mini whiteboards. Most students will probably evaluate the product, which will lead into using the prime factor form.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Complete the statement. A number that is a multiple of two or more numbers is called a multiple.

      Correct Answer: common

      Q2.
      Match each number with its first four multiples.

      Correct Answer:First four multiples of 2:,2, 4, 6, 8

      2, 4, 6, 8

      Correct Answer:First four multiples of 4:,4, 8, 12, 16

      4, 8, 12, 16

      Correct Answer:First four multiples of 3:,3, 6, 9, 12

      3, 6, 9, 12

      Correct Answer:First four multiples of 12:,12, 24, 36, 48

      12, 24, 36, 48

      Q3.
      Which of the following is a factor of $$2^3\times3^4\times5^2$$ and of $$2^3\times3^5\times5$$?

      $$2^3\times3^5\times5^2$$
      Correct answer: $$2^2\times3^4\times5$$
      $$2^3\times3^4\times5^2$$

      Q4.
      Select the correct statements.

      An image in a quiz
      Correct answer: 240 as a product of prime factors is $$2^4 \times 3 \times 5$$
      240 as a product of prime factors is $$2^2 \times 3^2 \times 5$$
      180 as a product of prime factors is $$2^2 \times 3 \times 5$$
      Correct answer: 180 as a product of prime factors is $$2^2 \times 3^2 \times 5$$

      Q5.
      The HCF of 84, 180 and 120 is .

      An image in a quiz
      Correct Answer: 12, twelve

      Q6.
      The HCF of 126, 945 and 189 is 63. The missing prime factor in the Venn diagram is .

      An image in a quiz
      Correct Answer: 7, seven

      6 Questions

      Q1.
      What does the L stand for in LCM?

      Correct Answer: lowest, least

      Q2.
      Which of the following is not a multiple of $$2\times3^2\times5$$?

      $$2^2\times3^2\times5$$
      $$2^2\times3^3\times5$$
      Correct answer: $$2^2\times3\times5$$
      $$2^2\times3^2\times5^3$$

      Q3.
      Given that $$12 = 2^2\times3$$, write 60 as a product of its prime factors.

      $$2^3\times3$$
      $$2^2\times3\times12$$
      $$2^2\times3^2\times5$$
      Correct answer: $$2^2\times3\times5$$

      Q4.
      The LCM of 18 and 30 is

      An image in a quiz
      Correct Answer: 90, ninety

      Q5.
      The LCM of 70 and 42 is 210. So, the missing prime factor in the Venn diagram is

      An image in a quiz
      Correct Answer: 7, seven

      Q6.
      The LCM of 12, 20 and 84 is

      An image in a quiz
      Correct Answer: 420, four hundred and twenty

      To help you plan your 7 maths lesson on: Lowest common multiple, download all teaching resources for free and adapt to suit your pupils' needs...