What is the Least Common Multiple of 77976 and 77984?
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 77976 and 77984 is 760110048.
LCM(77976,77984) = 760110048
Least Common Multiple of 77976 and 77984 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77976 and 77984, than apply into the LCM equation.
GCF(77976,77984) = 8
LCM(77976,77984) = ( 77976 × 77984) / 8
LCM(77976,77984) = 6080880384 / 8
LCM(77976,77984) = 760110048
Least Common Multiple (LCM) of 77976 and 77984 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 77976 and 77984. First we will calculate the prime factors of 77976 and 77984.
Prime Factorization of 77976
Prime factors of 77976 are 2, 3, 19. Prime factorization of 77976 in exponential form is:
77976 = 23 × 33 × 192
Prime Factorization of 77984
Prime factors of 77984 are 2, 2437. Prime factorization of 77984 in exponential form is:
77984 = 25 × 24371
Now multiplying the highest exponent prime factors to calculate the LCM of 77976 and 77984.
LCM(77976,77984) = 25 × 33 × 192 × 24371
LCM(77976,77984) = 760110048
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