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 |
|---|---|
| 115 and 90 | 2070 |
| 188 and 111 | 20868 |
| 38 and 69 | 2622 |
| 19 and 31 | 589 |
| 76 and 167 | 12692 |