Egypt Primary 6 Mathematics, Week 2: Finding the least common multiple of two numbers

GCF, LCM and fraction sums

Week 2 · Writing sums with the GCF; the LCM and fractions with unlike denominators · 3 lessons

Finding the least common multiple of two numbers

Discover Mathematics P6: Term 1, Unit 1, Lessons 3–4

GoalFind the LCM of two numbers by listing multiples and by using prime factors.

New words

multiple · what you get when you multiply a number by 1, 2, 3, …common multiple · a number that is a multiple of both numbersLCM · the smallest common multiple

Explanation

The multiples of a number are the answers in its times table: 4, 8, 12, 16 … A number that is a multiple of both 4 and 6 is a common multiple, and the smallest of them is the LCM. Method 1: list the multiples of each number and stop at the first one they share. Method 2: use the Venn diagram of the prime factors and multiply ALL the numbers in the diagram, counting the shared ones once. The LCM is not simply the two numbers multiplied: 4 × 6 = 24 is a common multiple, but 12 is smaller. Use the GCF when you split into equal groups, and the LCM when two repeating things meet again.

★Remember

GCF: split into equal groups. LCM: when do two repeating things meet again?

Worked examples

	1st	2nd	3rd	4th	5th
Multiples of 4	4	8	12	16	20
Multiples of 6	6	12	18	24	30

LCM of 4 and 6 by listing. Multiples of 4: 4, 8, 12, 16, 20. Multiples of 6: 6, 12, 18, 24, 30. The first number in both lists is 12, so the LCM is 12.

Two lanterns start blinking together. One blinks every 15 seconds and the other every 20 seconds. 15 = 3 × 5 and 20 = 2 × 2 × 5 share a 5. LCM = 5 × 3 × 2 × 2 = 60, so they blink together again after 60 seconds.

Question	Tool	Answer
Most equal groups of 6 and 8	GCF	2
Buses every 6 and 8 min meet again	LCM	24 min

Which one do I need? Sharing 6 and 8 into the most equal groups: GCF = 2. Buses that leave every 6 and every 8 minutes and start together: LCM = 24 minutes, because 24 = 6 × 4 = 8 × 3.

Class activity

Hopping game. Draw a number line to 30 on the floor with chalk. One child hops in 4s and another hops in 6s, both starting at 0. Stand on every landing spot. Where do both hop on the same number for the first time?

Practice

Find the LCM of 3 and 5.

Find the LCM of 8 and 12. Use the diagram of 8 = 2 × 2 × 2 and 12 = 2 × 2 × 3.

Find the LCM of 9 and 6.

A metro train comes every 10 minutes and a bus every 15 minutes. Both are at the stop at 7:00. When will they be there together again?

Hazem says the LCM of 6 and 9 is 54. Is that right?