Week 10 · Factors, primes and multiples · 3 lessons
3
Multiples and how they link to factors
Discover Mathematics P4: Term 1, Unit 6, Lessons 1–6
GoalList multiples, find common multiples and the lowest common multiple, and see how multiples and factors are related.
New words
multiple · the product of a number and a counting number: 4, 8, 12… are multiples of 4common multiple · a number that is a multiple of two or more numberslowest common multiple (LCM) · the first common multiple
Explanation
The multiples of a number come from skip counting: 4, 8, 12, 16, 20, 24, … They go on for ever. The multiples of 6 are 6, 12, 18, 24, 30, 36, … Numbers that are in both lists are common multiples: 12, 24 and 36. The first one, 12, is the lowest common multiple (LCM). Multiples and factors are linked. 12 is a multiple of 3 and of 4, and 3 and 4 are factors of 12. A number has only a few factors but endless multiples. The LCM helps with repeating events. Two lanterns blink every 4 seconds and every 6 seconds. They blink together after 12 seconds, and again after 24 seconds.
Worked examples
The multiples of 4 up to 36 are 4, 8, 12, 16, 20, 24, 28, 32 and 36. Each one is 4 more than the one before.
Number
Multiples
4
4, 8, 12, 16, 20, 24
6
6, 12, 18, 24, 30, 36
Find the LCM of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, 24. Multiples of 6: 6, 12, 18, 24. The common multiples are 12 and 24, and the lowest is 12.
A bus to Giza leaves every 15 minutes and a bus to Fayoum leaves every 20 minutes. Both leave at 6:00 a.m. The multiples of 15 are 15, 30, 45, 60. The multiples of 20 are 20, 40, 60. The LCM is 60, so they leave together again at 7:00 a.m.
Class activity
Skip-count race. Two players count aloud, one by 3s and one by 4s, and clap when both say the same number. Which numbers do you clap at? What is the first one? Play with 5 and 10, and with 6 and 8.
Practice
1
Write the first six multiples of 7.
7, 14, 21, 28, 35, 42.
2
Find the LCM of 3 and 5.
Multiples of 3: 3, 6, 9, 12, 15. Multiples of 5: 5, 10, 15. LCM = 15.
3
Find the LCM of 6 and 8.
Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. LCM = 24.
4
Is 40 a multiple of 8? Is 8 a factor of 40? Explain.
Yes to both: 5 × 8 = 40. 40 is a multiple of 8 and 8 is a factor of 40.
5
Two lights flash every 10 s and every 15 s. They flash together at 0 s. When do they next flash together?
