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What is the Least Common Multiple of 67760 and 67765?

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 67760 and 67765 is 918351280.

LCM(67760,67765) = 918351280

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Least Common Multiple of 67760 and 67765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67760 and 67765, than apply into the LCM equation.

GCF(67760,67765) = 5
LCM(67760,67765) = ( 67760 × 67765) / 5
LCM(67760,67765) = 4591756400 / 5
LCM(67760,67765) = 918351280

Least Common Multiple (LCM) of 67760 and 67765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67760 and 67765. First we will calculate the prime factors of 67760 and 67765.

Prime Factorization of 67760

Prime factors of 67760 are 2, 5, 7, 11. Prime factorization of 67760 in exponential form is:

67760 = 24 × 51 × 71 × 112

Prime Factorization of 67765

Prime factors of 67765 are 5, 13553. Prime factorization of 67765 in exponential form is:

67765 = 51 × 135531

Now multiplying the highest exponent prime factors to calculate the LCM of 67760 and 67765.

LCM(67760,67765) = 24 × 51 × 71 × 112 × 135531
LCM(67760,67765) = 918351280