LCM means Lowest Common Multiple and HCF means Highest Common Factor. There sre 4 parts to this:
Basic LCM:
Find the LCM of 4, 6 and 8.
First we list the first 6 multiples of 4, 6 and 8:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28
Multiples of 6: 6, 12, 18, 24, 30, 36,
Multiples of 8: 8, 16, 24, 32, 40, 48
As you can see, 24 is the lowest one that is in all 3. If there isn't one in the first 6, you'll have to keep adding more until you find one.
2. Real-life LCM:
Marcus visits Emily every 3 days. Rose visits Emily every 5 days. If they both visit Emily today, how many days will it be before they both visit on the same day again?
This is telling us to find the LCM of 3 and 5 - which will be when their "paths cross" and they both visit Emily on the same day. Let's start by listing the first 6 multiples of 3 and 5:
Multiples of 3: 3, 6, 9, 12, 15, 18
Multiples of 5: 5, 10, 15, 20, 25, 30
Here, 15 is the lowest common multiple, so it will be 15 days before they both visit Emily on the same day.
3. Basic HCF:
Find the HCF of 6, 8 and 16.
Here, we list ALL the factors of 6, 8 and 16:
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
Factors of 16: 1, 2, 4, 8, 16
There are 2 common factors here - 1 and 2. However, we want the HIGHEST common factor, so it must be 2.
4. Real-life HCF (Higher tier only):
Kiera is dividing counters into equal piles. She has 207 red counters and 253 blue counters. Each pile must contain only one colour of counters. What is the lowest number of piles she can make in total?
Here, we want the HIGHEST number that both counters will divide by, and this will be the number of counters in each pile. Let's do this first.
We want the factors of 207 and 253:
Factors of 207: 1, 3, 9, 23, 69, 207
Factors of 253: 1, 11, 23, 253
The highest common factor here is 23, so there are 23 counters in each pile. But remember, the question asked us for the number of piles.
To find this, we need to know the total number of counters, which is:
207 + 253 = 460.
We then divide 460 by 23 to get the number of piles.
460/23 = 20.
So Kiera has to make at least 20 piles. She could make more, though - but only if she put just 1 counter in each pile! This is complex, so you might need to read it over a few times.
Here is a quick quiz on all of these - just skip the last one if you're doing foundation.
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