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What is the Least Common Multiple of 30534 and 30546?

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 30534 and 30546 is 155448594.

LCM(30534,30546) = 155448594

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Least Common Multiple of 30534 and 30546 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30534 and 30546, than apply into the LCM equation.

GCF(30534,30546) = 6
LCM(30534,30546) = ( 30534 × 30546) / 6
LCM(30534,30546) = 932691564 / 6
LCM(30534,30546) = 155448594

Least Common Multiple (LCM) of 30534 and 30546 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30534 and 30546. First we will calculate the prime factors of 30534 and 30546.

Prime Factorization of 30534

Prime factors of 30534 are 2, 3, 7, 727. Prime factorization of 30534 in exponential form is:

30534 = 21 × 31 × 71 × 7271

Prime Factorization of 30546

Prime factors of 30546 are 2, 3, 1697. Prime factorization of 30546 in exponential form is:

30546 = 21 × 32 × 16971

Now multiplying the highest exponent prime factors to calculate the LCM of 30534 and 30546.

LCM(30534,30546) = 21 × 32 × 71 × 7271 × 16971
LCM(30534,30546) = 155448594