Least Common Multiple (LCM) of 123 and 156
The least common multiple (LCM) of 123 and 156 is 6396.
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 123 and 156?
First, calculate the GCD of 123 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 156 = 0 remainder 123 |
| 2 | 156 ÷ 123 = 1 remainder 33 |
| 3 | 123 ÷ 33 = 3 remainder 24 |
| 4 | 33 ÷ 24 = 1 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 108 | 3996 |
| 132 and 114 | 2508 |
| 20 and 186 | 1860 |
| 33 and 181 | 5973 |
| 197 and 15 | 2955 |