Least Common Multiple (LCM) of 150 and 59
The least common multiple (LCM) of 150 and 59 is 8850.
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 59?
First, calculate the GCD of 150 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 59 = 2 remainder 32 |
| 2 | 59 ÷ 32 = 1 remainder 27 |
| 3 | 32 ÷ 27 = 1 remainder 5 |
| 4 | 27 ÷ 5 = 5 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 182 | 4550 |
| 41 and 180 | 7380 |
| 126 and 193 | 24318 |
| 35 and 122 | 4270 |
| 135 and 82 | 11070 |