What do LCM and GCF mean?

Answer 1

Factors go into numbers, numbers go into multiples.

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder.

Answer 2

The LCM is the Lowest Common Multiple; it is the smallest number that is a common multiple of the given numbers.

Example.

Calculate the LCM of 4 and 6.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, ...

=> The common multiples of 4 and 6 are 12, 24, 36, ...

=> The Lowest Common Multiple of 4 and 6 is 12.

The gcd is the Greatest Common Divisor; it the the largest number that divides exactly into the given numbers.

Example.

Calculate the gcd of 28 and 70

The divisors of 28 are 1, 2, 4, 7, 14, 28.

The divisors of 70 are 1, 2, 5, 7, 14, 35, 70.

=> The common divisors are 1, 2, 7, 14.

=> The Greatest Common Divisor of 28 and 70 is 14.

The LCM is sometimes called the LCD - Lowest Common Denominator - especially when dealing with adding or subtracting fractions where a common denominator is required.

The GCD is also called the GCF - Greatest Common Factor - or HCF - Highest Common Factor.

Answer 3

GCF stands for Greatest Common Factor, and is the largest whole number that is a factor of two or more given numbers. LCM stands for Least Common Multiple, and is the smallest whole number that is a multiple of two or more given numbers.

Answer 4

The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. Factors go into numbers, numbers go into multiples.