Least Common Multiple (LCM) of 111 and 136
The least common multiple (LCM) of 111 and 136 is 15096.
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 136?
First, calculate the GCD of 111 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 136 = 0 remainder 111 |
| 2 | 136 ÷ 111 = 1 remainder 25 |
| 3 | 111 ÷ 25 = 4 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 75 | 975 |
| 90 and 51 | 1530 |
| 69 and 175 | 12075 |
| 71 and 140 | 9940 |
| 142 and 116 | 8236 |