Least Common Multiple (LCM) of 150 and 157
The least common multiple (LCM) of 150 and 157 is 23550.
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 157?
First, calculate the GCD of 150 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 157 = 0 remainder 150 |
| 2 | 157 ÷ 150 = 1 remainder 7 |
| 3 | 150 ÷ 7 = 21 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 109 | 7303 |
| 103 and 111 | 11433 |
| 130 and 78 | 390 |
| 172 and 110 | 9460 |
| 41 and 200 | 8200 |