Egypt Primary 5 Mathematics, Week 5: Multiples and the least common multiple

Prime factors, common factors and common multiples

Week 5 · Prime factors, greatest common factor and least common multiple · 3 lessons

Multiples and the least common multiple

Discover Mathematics P5: Term 1, Unit 2, Lessons 6–10

GoalList multiples, find common multiples and find the least common multiple of two numbers up to 12.

New words

multiple · a number you get when you multiply a number by 1, 2, 3, 4 and so oncommon multiple · a number that is a multiple of two or more numbersleast common multiple (LCM) · the smallest common multiple of two numbers

Explanation

The multiples of a number are found by skip counting. The multiples of 4 are 4, 8, 12, 16, 20, 24, … and they never end. The multiples of 6 are 6, 12, 18, 24, 30, … Numbers that appear in both lists are common multiples: 12, 24, 36, … The smallest of them is the least common multiple, so the LCM of 4 and 6 is 12. To find it, list the multiples of the bigger number and stop at the first one that the other number divides exactly. For 9 and 12: 12, 24, 36. Is 12 a multiple of 9? No. 24? No. 36? Yes, 9 × 4 = 36, so the LCM is 36. A multiple is never smaller than the number itself, but a factor is never bigger.

Number	×1	×2	×3	×4	×5	×6
4	4	8	12	16	20	24
6	6	12	18	24	30	36

Worked examples

Number	×1	×2	×3	×4
6	6	12	18	24
8	8	16	24	32

A red bus leaves a stop every 6 minutes and a blue bus every 8 minutes. They leave together now. Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The first common multiple is 24, so they leave together again after 24 minutes.

Mina buys notebooks in packs of 5 and pens in packs of 8. What is the smallest number of each that gives equal numbers of notebooks and pens? It is the LCM of 5 and 8. Multiples of 8: 8, 16, 24, 32, 40. 40 is a multiple of 5 (5 × 8). So 40 notebooks (8 packs) and 40 pens (5 packs).

✓Tip

Two numbers always have a common multiple: their product. But the LCM can be much smaller.

Find the LCM of 9 and 12. Multiples of 12: 12, 24, 36. 12 ÷ 9 and 24 ÷ 9 leave remainders, but 36 ÷ 9 = 4 exactly. So the LCM of 9 and 12 is 36.

Class activity

Jumping frogs. Draw a number line from 0 to 40. Colour the jumps of a frog that jumps 4 at a time in red, and the jumps of a frog that jumps 6 at a time in blue. Mark the points where both frogs land. Which is the first one? That is the LCM. Try 3 and 5 next.

Practice

Write the first six multiples of 7.

Find the LCM of 3 and 5.

Find the LCM of 4 and 10.

Find the LCM of 6 and 9.

One lamp flashes every 3 seconds and another every 4 seconds. They flash together at the start. How many times do they flash together in the next 36 seconds?