What is the Least Common Multiple of 415 and 434?
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 415 and 434 is 180110.
LCM(415,434) = 180110
Least Common Multiple of 415 and 434 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 415 and 434, than apply into the LCM equation.
GCF(415,434) = 1
LCM(415,434) = ( 415 × 434) / 1
LCM(415,434) = 180110 / 1
LCM(415,434) = 180110
Least Common Multiple (LCM) of 415 and 434 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 415 and 434. First we will calculate the prime factors of 415 and 434.
Prime Factorization of 415
Prime factors of 415 are 5, 83. Prime factorization of 415 in exponential form is:
415 = 51 × 831
Prime Factorization of 434
Prime factors of 434 are 2, 7, 31. Prime factorization of 434 in exponential form is:
434 = 21 × 71 × 311
Now multiplying the highest exponent prime factors to calculate the LCM of 415 and 434.
LCM(415,434) = 51 × 831 × 21 × 71 × 311
LCM(415,434) = 180110
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