Least Common Multiple (LCM) of 157 and 109
The least common multiple (LCM) of 157 and 109 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 157 and 109?
First, calculate the GCD of 157 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 109 = 1 remainder 48 |
| 2 | 109 ÷ 48 = 2 remainder 13 |
| 3 | 48 ÷ 13 = 3 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 29 | 2871 |
| 189 and 89 | 16821 |
| 161 and 123 | 19803 |
| 67 and 98 | 6566 |
| 96 and 152 | 1824 |