Introduction
The Least Common Multiple (LCM) is the smallest common multiple of any two or more numbers will divide evenly. The L.C.M of two numbers is the lowest number that can be divided both. It is used to find the lowest common denominator when adding or subtracting fractions.
Example:
Find the LCM of 2 and 4?
Given:
2 =2x1
=1x2
4= 2x2
LCM is 2x2=4
Finding Lcm: Steps
• Write the multiples of each of the numbers.
• Write the common multiples.
• Choose the least number, which is the LCM.
Example:
Find the LCM of 6 and 12?
Multiples of 6 are - 6, 12, 18, 24, 30, 36
Multiples of 12 are - 12, 24, 36, 48
Common multiples are - 12, 24, 36
Least common multiple or LCM is 12.
Methods
They are different methods to find the LCM of given numbers:
1) Prime factors
2) Greatest common factor
Prime Factors Method
Prime factors of a positive integer are prime numbers that divide that integer exactly, without leaving a remainder. The process of finding prime numbers is called integer factorization, or prime factorization.
Steps:
List out the prime factors for given digit
Multiply each factor with the greatest number of times it occurs
If the same factor occurs twice then multiply with greatest number times it occur.
Example:
List out the prime factors for 12
12 which can be written as:
12= 2x2x3
Greatest Common Factor Method
The largest number that divides evenly into each of a given set of numbers. Also called greatest common factor (GCF or GCD), highest common factor(HCF)
• Find the Greatest Common Factor (GCF) of the numbers
• Multiply the numbers together
• Divide the product of the numbers by the GCF.
Find the Lcm of 3 and 9
Given:
3=3x1
=1x3
9=3x3
=3x1x3x1
Factors of 3 and 9 are 1x3x3x1x3x1
LCM of 3 and 9 are: 3x3x1x1
LCM of 3 and 9 is 9.
Find the Lcm of 15 and 12 Using Gcd Method
Given:
15 and 12
15=5x3
12=3x4
Greatest common factor is 3
Divide one of the numbers by the G CF and multiply the answer times the other number.
15/3=5
12x5=60
Find the Lcm of 5,10,20?
Prime factors of given numbers are:
5=5x1
10=5x2
20=5x4
=5x2x2
Multiples of 5,10,20 are:
5x1x5x2x5x2x2
LCM of 5,10,20 are:
5x2x2=20