If the H.C.F. of two numbers is 12 and their L.C.M. is 144, what is the product

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Question: If the H.C.F. of two numbers is 12 and their L.C.M. is 144, what is the product of the two numbers?

Options:

Correct Answer: 1728

Solution:

The product of the two numbers is 1728 (H.C.F. * L.C.M. = 12 * 144).

If the H.C.F. of two numbers is 12 and their L.C.M. is 144, what is the product of the two numbers?

If the H.C.F. of two numbers is 12 and their L.C.M. is 144, what is the product of the two numbers?

Step 1: Understand that H.C.F. stands for Highest Common Factor and L.C.M. stands for Lowest Common Multiple.
Step 2: Note the values given in the question: H.C.F. = 12 and L.C.M. = 144.
Step 3: Recall the formula that states the product of two numbers is equal to the H.C.F. multiplied by the L.C.M.
Step 4: Use the formula: Product of the two numbers = H.C.F. * L.C.M.
Step 5: Substitute the values into the formula: Product = 12 * 144.
Step 6: Calculate the product: 12 * 144 = 1728.
Step 7: Conclude that the product of the two numbers is 1728.

H.C.F. and L.C.M. – Understanding the relationship between the Highest Common Factor (H.C.F.) and the Least Common Multiple (L.C.M.) of two numbers, specifically that the product of the two numbers equals the product of their H.C.F. and L.C.M.