Least Common Multiple (LCM) of 150 and 172
The least common multiple (LCM) of 150 and 172 is 12900.
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 172?
First, calculate the GCD of 150 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 172 = 0 remainder 150 |
| 2 | 172 ÷ 150 = 1 remainder 22 |
| 3 | 150 ÷ 22 = 6 remainder 18 |
| 4 | 22 ÷ 18 = 1 remainder 4 |
| 5 | 18 ÷ 4 = 4 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 65 | 8970 |
| 170 and 27 | 4590 |
| 123 and 43 | 5289 |
| 175 and 41 | 7175 |
| 96 and 36 | 288 |