Least Common Multiple (LCM) of 157 and 45
The least common multiple (LCM) of 157 and 45 is 7065.
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 45?
First, calculate the GCD of 157 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 45 = 3 remainder 22 |
| 2 | 45 ÷ 22 = 2 remainder 1 |
| 3 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 35 | 3815 |
| 197 and 76 | 14972 |
| 100 and 162 | 8100 |
| 98 and 91 | 1274 |
| 86 and 195 | 16770 |