Least Common Multiple (LCM) of 109 and 157
The least common multiple (LCM) of 109 and 157 is 17113.
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 109 and 157?
First, calculate the GCD of 109 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 157 = 0 remainder 109 |
| 2 | 157 ÷ 109 = 1 remainder 48 |
| 3 | 109 ÷ 48 = 2 remainder 13 |
| 4 | 48 ÷ 13 = 3 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 39 | 2145 |
| 75 and 20 | 300 |
| 136 and 97 | 13192 |
| 82 and 84 | 3444 |
| 37 and 84 | 3108 |