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What is the product of the least common multiple and the greatest common factor of $22$ and $48$?

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Answer:

1056

Explanation:

The least common multiple(LCM) of 22 and 48 is the smallest positive number that is divisible by both 22 and 48

The greatest common factor(GCF) of 22 and 48 is the largest positive integer that divides 22 and 48 without a remainder

To find LCM of 22 and 48

Find the prime factors of 22 and 48
Prime factorization of 22 ⇒ 2 x 11
Prime factorization of 48 ⇒ 2 x 2 x 2 x 2x 3


Multiply each factor the greatest number of times it appears in either 22 or 48

Factor 2 appears 4 times in 48 and only once in 22 => 2 x 2 x 2 x 2
Factor 11 appears 1 time in 22 and 0 times in 48: 11
Factor 3 appears 1 time in 48 and 0 times in 22: 3

Multiply these:
2 x 2 x 2 x 2 x 11 x 3

= 528

LCM (22, 48) = 528

To find GCF
Here we proceed as above by finding the prime factors of 22 and 48

But we only take the highest factor that is common to both 22 and 48

22 => 2 x 11

48 => 2 x 2 x 2 x 2 x 3

The highest factor common to both 22 and 48 is 2

GCF(22, 48) = 2

Product of LCM(22, 48) and GCF(22, 48)
= 528 x 2
= 1056

User Eugene Laminskiy
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