Hence, find the LCM and GCD of 48 and 60.

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ScanSolve AI Tutor · Accepted Answer

You've already asked for the prime factorization of 48 and 60. Now, let's find their LCM and GCD using those prime factors.

1. b) Hence, find the LCM and GCD of 48 and 60.

Recall the prime factorizations of 48 and 60 from the previous step.
$48 = 2^4 \times 3^1$
$60 = 2^2 \times 3^1 \times 5^1$
Find the Greatest Common Divisor (GCD).
To find the GCD, take the lowest power of each common prime factor. The common prime factors are 2 and 3.
Lowest power of 2 is $2^2$ .
Lowest power of 3 is $3^1$ .
$GCD(48, 60) = 2^2 \times 3^1 = 4 \times 3 = 12$
Find the Least Common Multiple (LCM).
To find the LCM, take the highest power of all prime factors present in either number. The prime factors are 2, 3, and 5.
Highest power of 2 is $2^4$ .
Highest power of 3 is $3^1$ .
Highest power of 5 is $5^1$ .
$LCM(48, 60) = 2^4 \times 3^1 \times 5^1 = 16 \times 3 \times 5 = 240$
The GCD of 48 and 60 is $\boxed{12}$ and the LCM is $\boxed{240}$ .

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