Least Common Multiple (LCM) of 137 and 112
The least common multiple (LCM) of 137 and 112 is 15344.
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 137 and 112?
First, calculate the GCD of 137 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 112 = 1 remainder 25 |
| 2 | 112 ÷ 25 = 4 remainder 12 |
| 3 | 25 ÷ 12 = 2 remainder 1 |
| 4 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 165 | 2145 |
| 76 and 30 | 1140 |
| 32 and 80 | 160 |
| 117 and 148 | 17316 |
| 15 and 173 | 2595 |