Least Common Multiple (LCM) of 132 and 123
The least common multiple (LCM) of 132 and 123 is 5412.
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 132 and 123?
First, calculate the GCD of 132 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 123 = 1 remainder 9 |
| 2 | 123 ÷ 9 = 13 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 109 | 12426 |
| 145 and 66 | 9570 |
| 10 and 70 | 70 |
| 32 and 27 | 864 |
| 75 and 183 | 4575 |