Least Common Multiple (LCM) of 157 and 85
The least common multiple (LCM) of 157 and 85 is 13345.
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 85?
First, calculate the GCD of 157 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 85 = 1 remainder 72 |
| 2 | 85 ÷ 72 = 1 remainder 13 |
| 3 | 72 ÷ 13 = 5 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 80 | 2960 |
| 73 and 88 | 6424 |
| 91 and 85 | 7735 |
| 101 and 146 | 14746 |
| 102 and 21 | 714 |