What is the Least Common Multiple of 76985 and 77000?
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 76985 and 77000 is 1185569000.
LCM(76985,77000) = 1185569000
Least Common Multiple of 76985 and 77000 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76985 and 77000, than apply into the LCM equation.
GCF(76985,77000) = 5
LCM(76985,77000) = ( 76985 × 77000) / 5
LCM(76985,77000) = 5927845000 / 5
LCM(76985,77000) = 1185569000
Least Common Multiple (LCM) of 76985 and 77000 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 76985 and 77000. First we will calculate the prime factors of 76985 and 77000.
Prime Factorization of 76985
Prime factors of 76985 are 5, 89, 173. Prime factorization of 76985 in exponential form is:
76985 = 51 × 891 × 1731
Prime Factorization of 77000
Prime factors of 77000 are 2, 5, 7, 11. Prime factorization of 77000 in exponential form is:
77000 = 23 × 53 × 71 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 76985 and 77000.
LCM(76985,77000) = 53 × 891 × 1731 × 23 × 71 × 111
LCM(76985,77000) = 1185569000
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