Least Common Multiple (LCM) of 157 and 119
The least common multiple (LCM) of 157 and 119 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 157 and 119?
First, calculate the GCD of 157 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 119 = 1 remainder 38 |
| 2 | 119 ÷ 38 = 3 remainder 5 |
| 3 | 38 ÷ 5 = 7 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 54 | 9126 |
| 148 and 163 | 24124 |
| 112 and 70 | 560 |
| 184 and 174 | 16008 |
| 13 and 117 | 117 |