If the LCM of two numbers is 84 and one of the numbers is 12, what is the other

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Question: If the LCM of two numbers is 84 and one of the numbers is 12, what is the other number?

Options:

Correct Answer: 28

Solution:

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 84 = (12 * b) / HCF. The other number is 28.

If the LCM of two numbers is 84 and one of the numbers is 12, what is the other number?

If the LCM of two numbers is 84 and one of the numbers is 12, what is the other number?

Correct Answer: 28

Step 1: Understand that LCM stands for Least Common Multiple, which is the smallest number that is a multiple of both numbers.
Step 2: We know the LCM of the two numbers is 84.
Step 3: One of the numbers is given as 12.
Step 4: We need to find the other number, which we will call 'b'.
Step 5: Use the formula for LCM: LCM = (a * b) / HCF, where 'a' is 12 and 'b' is the unknown number.
Step 6: Rearrange the formula to find 'b': b = (LCM * HCF) / a.
Step 7: We don't know HCF (Highest Common Factor) yet, but we can find it by knowing that LCM * HCF = a * b.
Step 8: Since we know LCM is 84 and 'a' is 12, we can express it as: 84 = (12 * b) / HCF.
Step 9: To find 'b', we can also use the fact that 12 and 'b' must multiply to a number that, when divided by their HCF, gives us 84.
Step 10: We can try different values for 'b' that are factors of 84 and see which one works with 12.
Step 11: Testing 28: LCM(12, 28) = 84, so 'b' is 28.

Least Common Multiple (LCM) – The LCM of two numbers is the smallest multiple that is evenly divisible by both numbers.
Highest Common Factor (HCF) – The HCF of two numbers is the largest number that divides both of them without leaving a remainder.
Relationship between LCM and HCF – The relationship between LCM and HCF can be expressed as LCM(a, b) = (a * b) / HCF(a, b).