Least Common Multiple (LCM) of 150 and 119
The least common multiple (LCM) of 150 and 119 is 17850.
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 119?
First, calculate the GCD of 150 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 119 = 1 remainder 31 |
| 2 | 119 ÷ 31 = 3 remainder 26 |
| 3 | 31 ÷ 26 = 1 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 141 | 14100 |
| 141 and 82 | 11562 |
| 65 and 43 | 2795 |
| 162 and 130 | 10530 |
| 134 and 134 | 134 |