Least Common Multiple (LCM) of 157 and 116
The least common multiple (LCM) of 157 and 116 is 18212.
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 157 and 116?
First, calculate the GCD of 157 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 116 = 1 remainder 41 |
| 2 | 116 ÷ 41 = 2 remainder 34 |
| 3 | 41 ÷ 34 = 1 remainder 7 |
| 4 | 34 ÷ 7 = 4 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 94 | 9024 |
| 179 and 129 | 23091 |
| 69 and 188 | 12972 |
| 117 and 143 | 1287 |
| 105 and 190 | 3990 |