Least Common Multiple (LCM) of 137 and 111
The least common multiple (LCM) of 137 and 111 is 15207.
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 111?
First, calculate the GCD of 137 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 111 = 1 remainder 26 |
| 2 | 111 ÷ 26 = 4 remainder 7 |
| 3 | 26 ÷ 7 = 3 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 58 | 3828 |
| 117 and 126 | 1638 |
| 60 and 163 | 9780 |
| 107 and 129 | 13803 |
| 168 and 197 | 33096 |