Powers, Indices, LCM and GCF
Primary 6 · Mathematics
Powers, Indices, LCM and GCF
Lesson 6 of 6
30 min
Let's begin
Byiringiro reads two problems. One asks when two bells will ring together again. The other asks for the biggest equal groups a class can make. “One needs the LCM and the other needs the GCF,” he says. “But which is which?”
| If the problem asks… | Use | Why |
|---|---|---|
| When will things happen together again? What is the smallest amount that several numbers all go into? | LCM | The answer is a multiple, so it is at least as big as the numbers. |
| What is the greatest number of equal groups? What is the largest equal piece or share? | GCF | The answer divides the numbers, so it is no bigger than them. |
For any two whole numbers: LCM × GCF = the first number × the second number.
Check with 12 and 18: LCM = 36 and GCF = 6. 36 × 6 = 216, and 12 × 18 = 216. ✔
Worked example 1
The GCF of two numbers is 6 and their LCM is 72. One number is 18. Find the other.
Worked example 2
Find the smallest number which leaves a remainder of 1 when divided by 4, by 6 or by 9.
Worked example 3
Find the greatest number that divides 50 and 74 and leaves a remainder of 2 each time.
Tip
Ask: will my answer be bigger or smaller than the numbers? Bigger (a time in the future, a total) → LCM. Smaller (a group size, a piece) → GCF.
Work each one in your exercise book first, then tap Show answer to check.
Two church bells ring every 15 minutes and every 25 minutes. They ring together at 6:00 a.m. When do they next ring together?
Answer: LCM(15, 25) = 75 minutes, so at 7:15 a.m.
A carpenter cuts two planks, 90 cm and 120 cm long, into equal pieces as long as possible with nothing left. How long is each piece?
Answer: GCF(90, 120) = 30 cm.
The LCM of two numbers is 60, their GCF is 4, and one number is 12. Find the other number.
Answer: 60 × 4 ÷ 12 = 20.
Find the smallest number that leaves a remainder of 3 when divided by 5 or by 8.
Answer: LCM(5, 8) + 3 = 43.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
Quick check
Two taps drip every 8 seconds and every 12 seconds. They drip together now. To find when they next drip together, what do you need?
