Least Common Multiple (LCM) of 111 and 137
The least common multiple (LCM) of 111 and 137 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 111 and 137?
First, calculate the GCD of 111 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 137 = 0 remainder 111 |
| 2 | 137 ÷ 111 = 1 remainder 26 |
| 3 | 111 ÷ 26 = 4 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 181 and 31 | 5611 |
| 148 and 128 | 4736 |
| 175 and 192 | 33600 |
| 14 and 122 | 854 |
| 161 and 83 | 13363 |