Divide the L.C.M of 48, 64 and 80 by their H.C.F

To solve this problem, we need to find the Least Common Multiple (L.C.M) and the Highest Common Factor (H.C.F) of the numbers 48, 64, and 80.

Step 1: Find the Prime Factors of each number

• 48: $2 \times 24 = 2^2 \times 12 = 2^3 \times 6 = 2^4 \times 3$
• 64: $2 \times 32 = 2^2 \times 16 = 2^3 \times 8 = 2^4 \times 4 = 2^5 \times 2 = 2^6$
• 80: $2 \times 40 = 2^2 \times 20 = 2^3 \times 10 = 2^4 \times 5$

Step 2: Calculate the H.C.F

The H.C.F is the product of the lowest power of each common prime factor.

• The only common prime factor is 2.
• The lowest power of 2 among $2^4, 2^6,$ and $2^4$ is $2^4$.
• H.C.F = $2^4 = 16$.

Step 3: Calculate the L.C.M

The L.C.M is the product of the highest power of every prime factor present in the numbers.

• The prime factors involved are 2, 3, and 5.
• Highest power of 2 is $2^6$.
• Highest power of 3 is $3^1$.
• Highest power of 5 is $5^1$.
• L.C.M = $2^6 \times 3 \times 5 = 64 \times 15 = 960$.

Step 4: Divide the L.C.M by the H.C.F

Now, we perform the final calculation as requested:

Comparing this result to the given options, we find that it matches option D.

Exam Tip: When finding the L.C.M and H.C.F of large numbers, prime factorization is much safer than listing multiples or factors, as it prevents you from missing a number and saves time during the JAMB exam.