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What is the Least Common Multiple of 1755 and 1772?

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 1755 and 1772 is 3109860.

LCM(1755,1772) = 3109860

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Least Common Multiple of 1755 and 1772 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1755 and 1772, than apply into the LCM equation.

GCF(1755,1772) = 1
LCM(1755,1772) = ( 1755 × 1772) / 1
LCM(1755,1772) = 3109860 / 1
LCM(1755,1772) = 3109860

Least Common Multiple (LCM) of 1755 and 1772 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1755 and 1772. First we will calculate the prime factors of 1755 and 1772.

Prime Factorization of 1755

Prime factors of 1755 are 3, 5, 13. Prime factorization of 1755 in exponential form is:

1755 = 33 × 51 × 131

Prime Factorization of 1772

Prime factors of 1772 are 2, 443. Prime factorization of 1772 in exponential form is:

1772 = 22 × 4431

Now multiplying the highest exponent prime factors to calculate the LCM of 1755 and 1772.

LCM(1755,1772) = 33 × 51 × 131 × 22 × 4431
LCM(1755,1772) = 3109860