Least Common Multiple (LCM) of 105 and 157
The least common multiple (LCM) of 105 and 157 is 16485.
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 105 and 157?
First, calculate the GCD of 105 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 157 = 0 remainder 105 |
| 2 | 157 ÷ 105 = 1 remainder 52 |
| 3 | 105 ÷ 52 = 2 remainder 1 |
| 4 | 52 ÷ 1 = 52 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 54 | 1674 |
| 180 and 117 | 2340 |
| 168 and 136 | 2856 |
| 156 and 130 | 780 |
| 26 and 172 | 2236 |