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What is the Least Common Multiple of 40080 and 40090?

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 40080 and 40090 is 160680720.

LCM(40080,40090) = 160680720

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Least Common Multiple of 40080 and 40090 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40080 and 40090, than apply into the LCM equation.

GCF(40080,40090) = 10
LCM(40080,40090) = ( 40080 × 40090) / 10
LCM(40080,40090) = 1606807200 / 10
LCM(40080,40090) = 160680720

Least Common Multiple (LCM) of 40080 and 40090 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40080 and 40090. First we will calculate the prime factors of 40080 and 40090.

Prime Factorization of 40080

Prime factors of 40080 are 2, 3, 5, 167. Prime factorization of 40080 in exponential form is:

40080 = 24 × 31 × 51 × 1671

Prime Factorization of 40090

Prime factors of 40090 are 2, 5, 19, 211. Prime factorization of 40090 in exponential form is:

40090 = 21 × 51 × 191 × 2111

Now multiplying the highest exponent prime factors to calculate the LCM of 40080 and 40090.

LCM(40080,40090) = 24 × 31 × 51 × 1671 × 191 × 2111
LCM(40080,40090) = 160680720