Least Common Multiple (LCM) of 157 and 195
The least common multiple (LCM) of 157 and 195 is 30615.
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 195?
First, calculate the GCD of 157 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 195 = 0 remainder 157 |
| 2 | 195 ÷ 157 = 1 remainder 38 |
| 3 | 157 ÷ 38 = 4 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 |
|---|---|
| 117 and 81 | 1053 |
| 87 and 42 | 1218 |
| 107 and 81 | 8667 |
| 26 and 185 | 4810 |
| 109 and 185 | 20165 |