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Maths Exercices

Least common multiple (LCM) and Greast common factor (GCF)


Greatest common factor (GCF):
To find the GCF of a set of numbers, you must factor each of the numbers into primes. Then for each different prime number in all of the factorizations, do the following...

1. Count the number of times each prime number appears in all the factorizations.
2. For each prime number, take the lowest of these counts and write the result.
3. The greatest common factor is the product of all the prime numbers written down.

GCF (4,6)=2, because 4=2·2 and 6=2·3,
The only number that appears in all the factorizations is 2.
That is, GCF(4,6)=2

If GCF(a,b)=1, is said that a and b are relative primes

Least common multiple (LCM):
To find the LCM of a set of numbers, you must factor each of the numbers into primes. Then for each different prime number in all of the factorizations, do the following...

1. Count the number of times each prime number appears in each of the factorizations.
2. For each prime number, take the largest of these counts and write the result.
3. The least common multiple is the product of all the prime numbers written down. (Remember taking the highest number of times they appear)

LCM (4,6)=12, because 4=2·2 and 6=2·3,
The highest number of times number 2 appears is 2
The highest number of times number 3 appears is 1.

So LCM(4,6)=2·2·3

Find the LCM and the GCF of the following numbers:
4 , 18 and 240 : GCF: LCM: