Powers, Indices, LCM and GCF
Primary 6 · Mathematics
Powers, Indices, LCM and GCF
Lesson 4 of 6
30 min
Let's begin
At Nyabugogo bus park, a bus to Musanze leaves every 12 minutes and a bus to Huye leaves every 18 minutes. At 7:00 a.m. both leave at the same moment. Niyonzima, who sells tickets, wants to know when they will next leave together.
The multiples of a number are the answers in its times table: the multiples of 4 are 4, 8, 12, 16, 20, 24, … A number that is a multiple of two numbers is a common multiple. The smallest one is the Lowest Common Multiple (LCM).
Worked example
LCM of 4 and 6.
Write each number as a product of primes. Take every prime that appears, using its highest power, and multiply.
Worked example
the buses, LCM of 12 and 18.
The buses leave together again after 36 minutes, at 7:36 a.m.
Worked example
with three numbers: LCM of 6, 8 and 10.
Worked example
At a school party, juice comes in packs of 6 bottles and cups come in packs of 8. What is the smallest number of each pack to buy so that there is exactly one cup for each bottle?
Look for words like together again, at the same time and smallest number that both …. They tell you to find the LCM.
Tip
LCM: Lots of Common Multiples, take the Lowest. The LCM is never smaller than the biggest of your numbers.
Work each one in your exercise book first, then tap Show answer to check.
Find the LCM of 8 and 10.
Answer: 40. Multiples of 10: 10, 20, 30, 40 … and 40 is the first one that 8 also divides.
Find the LCM of 9 and 15 using prime factors.
Answer: 9 = 3², 15 = 3 × 5, so LCM = 3² × 5 = 45.
Find the LCM of 4, 5 and 6.
Answer: 60.
Two lights flash together. One flashes every 6 seconds and the other every 10 seconds. After how many seconds do they flash together again?
Answer: LCM(6, 10) = 30 seconds.
What you learned today
Sources and credits
The stories, Rwandan worked examples and practice questions were written by Ganzaa.
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