Least Common Multiple (LCM) of 150 and 123
The least common multiple (LCM) of 150 and 123 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 150 and 123?
First, calculate the GCD of 150 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 123 = 1 remainder 27 |
| 2 | 123 ÷ 27 = 4 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 165 | 7920 |
| 191 and 182 | 34762 |
| 194 and 55 | 10670 |
| 170 and 78 | 6630 |
| 91 and 12 | 1092 |