Least Common Multiple (LCM) of 106 and 157
The least common multiple (LCM) of 106 and 157 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 106 and 157?
First, calculate the GCD of 106 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 157 = 0 remainder 106 |
| 2 | 157 ÷ 106 = 1 remainder 51 |
| 3 | 106 ÷ 51 = 2 remainder 4 |
| 4 | 51 ÷ 4 = 12 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 77 | 10318 |
| 12 and 72 | 72 |
| 16 and 73 | 1168 |
| 52 and 110 | 2860 |
| 100 and 68 | 1700 |