Least Common Multiple (LCM) of 157 and 185
The least common multiple (LCM) of 157 and 185 is 29045.
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 185?
First, calculate the GCD of 157 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 185 = 0 remainder 157 |
| 2 | 185 ÷ 157 = 1 remainder 28 |
| 3 | 157 ÷ 28 = 5 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 145 | 8120 |
| 157 and 109 | 17113 |
| 17 and 114 | 1938 |
| 121 and 197 | 23837 |
| 192 and 132 | 2112 |