If the least common multiple (LCM) of two numbers is 60 and one of the numbers i

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Question: If the least common multiple (LCM) of two numbers is 60 and one of the numbers is 15, what could be the other number?

Options:

Correct Answer: 30

Solution:

The LCM of 15 and 20 is 60, making 20 a valid option. 30 and 60 would not work as they would exceed the LCM.

If the least common multiple (LCM) of two numbers is 60 and one of the numbers is 15, what could be the other number?

If the least common multiple (LCM) of two numbers is 60 and one of the numbers is 15, what could be the other number?

Step 1: Understand that the least common multiple (LCM) of two numbers is the smallest number that both numbers can divide into without leaving a remainder.
Step 2: We know one number is 15 and the LCM is 60.
Step 3: To find the other number, we need to find a number that, when combined with 15, gives an LCM of 60.
Step 4: List the multiples of 15: 15, 30, 45, 60, ...
Step 5: Check which of these multiples can combine with another number to give an LCM of 60.
Step 6: The number 20 can be checked: LCM(15, 20) = 60, so 20 is a valid option.
Step 7: Check other numbers like 30 and 60: LCM(15, 30) = 30 (not valid), LCM(15, 60) = 60 (but 60 is not less than 60).
Step 8: Conclude that the other number could be 20.

Least Common Multiple (LCM) – The least common multiple of two numbers is the smallest number that is a multiple of both numbers.
Divisibility – Understanding how numbers divide into each other is crucial for determining possible candidates for the other number.
Factors – Recognizing the factors of the given numbers helps in identifying potential candidates for the other number.