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

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

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

Steps: 11

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.