Least Common Multiple (LCM) of 157 and 114
The least common multiple (LCM) of 157 and 114 is 17898.
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 114?
First, calculate the GCD of 157 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 114 = 1 remainder 43 |
| 2 | 114 ÷ 43 = 2 remainder 28 |
| 3 | 43 ÷ 28 = 1 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 85 | 1190 |
| 128 and 126 | 8064 |
| 122 and 194 | 11834 |
| 137 and 121 | 16577 |
| 116 and 122 | 7076 |