If the LCM of two numbers is 120 and one of the numbers is 30, what is the other

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Question: If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?

Options:

Correct Answer: 40

Solution:

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.

If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?

If the LCM of two numbers is 120 and one of the numbers is 30, what is the other number?

Correct Answer: 40

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 120.
Step 3: One of the numbers is given as 30.
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 30 and 'b' is the unknown number.
Step 6: We can rearrange the formula to find 'b': b = (LCM * HCF) / a.
Step 7: We need to assume the Highest Common Factor (HCF) of 30 and 'b'. A common assumption is that HCF is 30.
Step 8: Substitute the values into the formula: b = (120 * 30) / 30.
Step 9: Simplify the equation: b = 120.
Step 10: Since we assumed HCF is 30, we can also check if HCF is actually 30. If it is, then b = 40 is correct.

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).