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What is the Least Common Multiple of 31201 and 31209?

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 31201 and 31209 is 973752009.

LCM(31201,31209) = 973752009

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Least Common Multiple of 31201 and 31209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31201 and 31209, than apply into the LCM equation.

GCF(31201,31209) = 1
LCM(31201,31209) = ( 31201 × 31209) / 1
LCM(31201,31209) = 973752009 / 1
LCM(31201,31209) = 973752009

Least Common Multiple (LCM) of 31201 and 31209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31201 and 31209. First we will calculate the prime factors of 31201 and 31209.

Prime Factorization of 31201

Prime factors of 31201 are 41, 761. Prime factorization of 31201 in exponential form is:

31201 = 411 × 7611

Prime Factorization of 31209

Prime factors of 31209 are 3, 101, 103. Prime factorization of 31209 in exponential form is:

31209 = 31 × 1011 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 31201 and 31209.

LCM(31201,31209) = 411 × 7611 × 31 × 1011 × 1031
LCM(31201,31209) = 973752009