Least Common Multiple (LCM) of 157 and 165
The least common multiple (LCM) of 157 and 165 is 25905.
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 165?
First, calculate the GCD of 157 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 165 = 0 remainder 157 |
| 2 | 165 ÷ 157 = 1 remainder 8 |
| 3 | 157 ÷ 8 = 19 remainder 5 |
| 4 | 8 ÷ 5 = 1 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 |
|---|---|
| 11 and 192 | 2112 |
| 97 and 88 | 8536 |
| 144 and 40 | 720 |
| 20 and 62 | 620 |
| 108 and 17 | 1836 |