Least Common Multiple (LCM) of 157 and 121
The least common multiple (LCM) of 157 and 121 is 18997.
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 121?
First, calculate the GCD of 157 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 121 = 1 remainder 36 |
| 2 | 121 ÷ 36 = 3 remainder 13 |
| 3 | 36 ÷ 13 = 2 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 151 | 5285 |
| 193 and 116 | 22388 |
| 82 and 155 | 12710 |
| 178 and 141 | 25098 |
| 98 and 53 | 5194 |