Least Common Multiple (LCM) of 119 and 157
The least common multiple (LCM) of 119 and 157 is 18683.
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 119 and 157?
First, calculate the GCD of 119 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 157 = 0 remainder 119 |
| 2 | 157 ÷ 119 = 1 remainder 38 |
| 3 | 119 ÷ 38 = 3 remainder 5 |
| 4 | 38 ÷ 5 = 7 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 109 | 21255 |
| 129 and 100 | 12900 |
| 17 and 98 | 1666 |
| 13 and 88 | 1144 |
| 155 and 130 | 4030 |