What is the difference between LCM and GCF. Explain in detail?

Answer 1

if u take 2*3=6
then 2 and 3 are called factors of 6, and 6 is said to be th emultiple of 2 and 3
now lets go further, every no. has atleast two factors, 1 and itself
if u take two numbers they may have one or many common factors. we know that the least common factor will be obviously 1. Therfore we look for the Greatest common Factor

similarly two numbers may have a common multiple eg, a common multiple of 2 and 3 is 6, another one is 12, 18 30 and so on
hence there is no upper limit
we therefor look for the least common multiple or LCM

hope i answer ur question

Answer 2

The greatest common factor (also called the greatest common divisor) of two numbers m and n is the *largest* number that divides both m and n. In other words (using the notation a|b, meaning a divides b), d is the greatest common divisor of m and n if d|m AND d|n and if any other number c|m and c|n then c|d (this shows d is the largest). The least common multiple, on the other hand, is the smallest number that is divisible by both m and n. So if k is the least common multiple, then m|k and n|k and if c is any other number such that m|c and n|c then k|c (making k the smallest).

Using numbers, you'll find that the greatest common disivor of 280 and 720 is 40, so 40|280 (280=7(40)) and 40|720 (720=18(40)) and you can check that any other number dividing both 280 and 720 must divide 40. On the other hand, their least common multiple is 5040 since 720|5040 (5040=7(720)) and 280|5040 (5040=18(280)) and you can check any other number that both 720 and 280 divide must also be divisible by 5040. I guess that's the best way to see the difference.

Also, the two notions are related by the formula:

lcm(m,n)=((m)(n))/(gcd(m,n)).

In words, the least common multiple of m and n is found by multiplying m and n together and then divising by the greatest common divisor of m and n.

Hope this helps to clear up any confusion!!

Answer 3

LCM means the Lowest Common Multiple.
It the number with the lowest value which is a multiple of 2 or more numbers. eg: 6 is the LCM of 3 and 2.
GCF means Greatest Common Factor.
It is the number which is the number with the greatest value and a factor of 2 or more numbers. eg: 6 is the GCF of 6 and 12.

Answer 4

lcm---- Least common denominator, first find the factors of given denomitors of fractions, eg 2/4, 3/6, find the fraction of 4=2x2, then 6=2x3 now take the common factor 2 of both fraction, multiply by remaining uncommon fractions 2x3= 12. HCF= find factors of denominators of fraction the same as above, then take only common factor 2, that is your GCF