Least Common Multiple (LCM) of 91 and 157
The least common multiple (LCM) of 91 and 157 is 14287.
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 91 and 157?
First, calculate the GCD of 91 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 157 = 0 remainder 91 |
| 2 | 157 ÷ 91 = 1 remainder 66 |
| 3 | 91 ÷ 66 = 1 remainder 25 |
| 4 | 66 ÷ 25 = 2 remainder 16 |
| 5 | 25 ÷ 16 = 1 remainder 9 |
| 6 | 16 ÷ 9 = 1 remainder 7 |
| 7 | 9 ÷ 7 = 1 remainder 2 |
| 8 | 7 ÷ 2 = 3 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 148 | 13172 |
| 103 and 60 | 6180 |
| 172 and 59 | 10148 |
| 197 and 71 | 13987 |
| 115 and 74 | 8510 |