
Least Common Multiple (LCM) of 96 and 123
The least common multiple (LCM) of 96 and 123 is 3936.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 96 and 123?
First, calculate the GCD of 96 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 96 ÷ 123 = 0 remainder 96 |
2 | 123 ÷ 96 = 1 remainder 27 |
3 | 96 ÷ 27 = 3 remainder 15 |
4 | 27 ÷ 15 = 1 remainder 12 |
5 | 15 ÷ 12 = 1 remainder 3 |
6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
192 and 10 | 960 |
109 and 35 | 3815 |
79 and 188 | 14852 |
78 and 118 | 4602 |
67 and 34 | 2278 |