Least Common Multiple (LCM) of 112 and 150
The least common multiple (LCM) of 112 and 150 is 8400.
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 112 and 150?
First, calculate the GCD of 112 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 150 = 0 remainder 112 |
| 2 | 150 ÷ 112 = 1 remainder 38 |
| 3 | 112 ÷ 38 = 2 remainder 36 |
| 4 | 38 ÷ 36 = 1 remainder 2 |
| 5 | 36 ÷ 2 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 54 | 918 |
| 87 and 73 | 6351 |
| 69 and 73 | 5037 |
| 127 and 119 | 15113 |
| 109 and 133 | 14497 |