Least Common Multiple (LCM) of 157 and 106
The least common multiple (LCM) of 157 and 106 is 16642.
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 106?
First, calculate the GCD of 157 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 106 = 1 remainder 51 |
| 2 | 106 ÷ 51 = 2 remainder 4 |
| 3 | 51 ÷ 4 = 12 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 128 | 5760 |
| 54 and 91 | 4914 |
| 84 and 135 | 3780 |
| 179 and 68 | 12172 |
| 109 and 189 | 20601 |