Least Common Multiple (LCM) of 137 and 100
The least common multiple (LCM) of 137 and 100 is 13700.
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 100?
First, calculate the GCD of 137 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 100 = 1 remainder 37 |
| 2 | 100 ÷ 37 = 2 remainder 26 |
| 3 | 37 ÷ 26 = 1 remainder 11 |
| 4 | 26 ÷ 11 = 2 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 104 | 11544 |
| 15 and 33 | 165 |
| 180 and 138 | 4140 |
| 57 and 121 | 6897 |
| 128 and 56 | 896 |