Least Common Multiple (LCM) of 100 and 137
The least common multiple (LCM) of 100 and 137 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 100 and 137?
First, calculate the GCD of 100 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 137 = 0 remainder 100 |
| 2 | 137 ÷ 100 = 1 remainder 37 |
| 3 | 100 ÷ 37 = 2 remainder 26 |
| 4 | 37 ÷ 26 = 1 remainder 11 |
| 5 | 26 ÷ 11 = 2 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 134 | 2680 |
| 37 and 112 | 4144 |
| 76 and 143 | 10868 |
| 198 and 58 | 5742 |
| 69 and 25 | 1725 |