Least Common Multiple (LCM) of 117 and 150
The least common multiple (LCM) of 117 and 150 is 5850.
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 117 and 150?
First, calculate the GCD of 117 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 150 = 0 remainder 117 |
| 2 | 150 ÷ 117 = 1 remainder 33 |
| 3 | 117 ÷ 33 = 3 remainder 18 |
| 4 | 33 ÷ 18 = 1 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 148 | 19092 |
| 55 and 139 | 7645 |
| 188 and 147 | 27636 |
| 174 and 193 | 33582 |
| 25 and 195 | 975 |