The Least Common Multiple (LCM) of two numbers, where one number is divisible by the other, is simply the larger of the two numbers.
Let's break down why this is the case:
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Understanding LCM: The LCM is the smallest positive integer that is perfectly divisible by both of the original numbers.
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Divisibility: When one number (let's call it 'a') is divisible by another number ('b'), it means 'a' is a multiple of 'b'. In other words, a = kb, where 'k' is an integer.
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Applying to LCM: Since 'a' is a multiple of 'b', 'a' is divisible by both 'a' and 'b'. Any multiple of 'a' will also be a multiple of 'b', but 'a' itself is the smallest such multiple.
Example:
Let's say we have the numbers 6 and 18. 18 is divisible by 6 (18 / 6 = 3).
- Multiples of 6: 6, 12, 18, 24, 30...
- Multiples of 18: 18, 36, 54...
The smallest number that appears in both lists (i.e., the LCM) is 18, which is the larger of the two numbers.
General Rule:
If 'x' is divisible by 'y', then LCM(x, y) = x.
