Number · Integers, powers & roots
Chapter 1 · 3
The idea
HCF and LCM
What highest common factor and lowest common multiple actually mean, how prime factors give both (lowest powers vs highest powers), and how to spot which one a word problem is asking for.
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Number · Integers, powers & roots
HCF and LCM
What highest common factor and lowest common multiple actually mean, how prime factors give both (lowest powers vs highest powers), and how to spot which one a word problem is asking for.
Why it works
Two numbers, two directions
Two numbers, two different questions. The HCF is the biggest number that divides into both — it's about breaking the numbers down, so it's at most the smaller number. The LCM is the smallest number both divide into — it's about building up, so it's at least the larger number.Keeping those directions straight kills the classic swap: the HCF of 72 and 120 can't be 360, because 360 doesn't divide into either.
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The rest of the explanation, plus 2 worked examples you step through move by move.
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