Least Common Multiple (LCM) of 111 and 154
The least common multiple (LCM) of 111 and 154 is 17094.
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 154?
First, calculate the GCD of 111 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 154 = 0 remainder 111 |
| 2 | 154 ÷ 111 = 1 remainder 43 |
| 3 | 111 ÷ 43 = 2 remainder 25 |
| 4 | 43 ÷ 25 = 1 remainder 18 |
| 5 | 25 ÷ 18 = 1 remainder 7 |
| 6 | 18 ÷ 7 = 2 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 80 | 5360 |
| 25 and 77 | 1925 |
| 79 and 64 | 5056 |
| 155 and 127 | 19685 |
| 132 and 154 | 924 |