Least Common Multiple (LCM) of 123 and 150
The least common multiple (LCM) of 123 and 150 is 6150.
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 150?
First, calculate the GCD of 123 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 150 = 0 remainder 123 |
| 2 | 150 ÷ 123 = 1 remainder 27 |
| 3 | 123 ÷ 27 = 4 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 |
|---|---|
| 151 and 102 | 15402 |
| 98 and 181 | 17738 |
| 69 and 192 | 4416 |
| 109 and 89 | 9701 |
| 39 and 196 | 7644 |