Least Common Multiple (LCM) of 150 and 112
The least common multiple (LCM) of 150 and 112 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 150 and 112?
First, calculate the GCD of 150 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 112 = 1 remainder 38 |
| 2 | 112 ÷ 38 = 2 remainder 36 |
| 3 | 38 ÷ 36 = 1 remainder 2 |
| 4 | 36 ÷ 2 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 19 | 760 |
| 109 and 185 | 20165 |
| 13 and 58 | 754 |
| 175 and 175 | 175 |
| 88 and 93 | 8184 |