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What is the Least Common Multiple of 33 and 53?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 33 and 53 is 1749.

LCM(33,53) = 1749

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Least Common Multiple of 33 and 53 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33 and 53, than apply into the LCM equation.

GCF(33,53) = 1
LCM(33,53) = ( 33 × 53) / 1
LCM(33,53) = 1749 / 1
LCM(33,53) = 1749

Least Common Multiple (LCM) of 33 and 53 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33 and 53. First we will calculate the prime factors of 33 and 53.

Prime Factorization of 33

Prime factors of 33 are 3, 11. Prime factorization of 33 in exponential form is:

33 = 31 × 111

Prime Factorization of 53

Prime factors of 53 are 53. Prime factorization of 53 in exponential form is:

53 = 531

Now multiplying the highest exponent prime factors to calculate the LCM of 33 and 53.

LCM(33,53) = 31 × 111 × 531
LCM(33,53) = 1749

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