Least Common Multiple (LCM) of 113 and 150
The least common multiple (LCM) of 113 and 150 is 16950.
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 113 and 150?
First, calculate the GCD of 113 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 150 = 0 remainder 113 |
| 2 | 150 ÷ 113 = 1 remainder 37 |
| 3 | 113 ÷ 37 = 3 remainder 2 |
| 4 | 37 ÷ 2 = 18 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 106 | 2014 |
| 22 and 29 | 638 |
| 65 and 51 | 3315 |
| 89 and 123 | 10947 |
| 171 and 139 | 23769 |