LCM (lowest common multiple)

[xavier]

could some one please tell me the lcm of 25 and 63, 32 and 15, 12 and 30. thankyou

[pinus]

As a first step you need to find the factors of the numbers 25 = 5*5 63 = 9*7 The lowest common multiple must include factors so that each of the original numbers can be created out if it. In this case we get 5*5*9*7 =1575 ======= 32 = 2*2*2*2*2 15 = 5*3 So LCM is 2*2*2*2*2*5*3 = 480 ======= 12 = 2*2*3 = 2*(2*3) 30 = 2*3*5 = 5*(2*3) In this case, both numbers are multiples of 6, so we only need to include 6 once. LCM 2*5*(2*3) = 60 ======= I hope this is not too confusing

[xavier]

thanks pinus

[DrP]

You don't actually need to factorize the numbers. All you need to do is find the GCD (greatest common divisor) of the numbers using Euclid's Algorithm: 63=2*25+13 25=1*13+12 13=12+1 12=12*1+0 so the GCD of 25 and 63 is 1. Therefore the LCM is 25*63/1=1575 32=2*15+2 15=7*2+1 2=2*1+0 so the GCD of 32 and 15 is 1. Therefore the LCM is 32*15/1=480 30=2*12+6 12=2*6+0 so the GCD of 30 and 12 is 6. Therefore the LCM is 30*12/6=60