Least Common Multiple (LCM) of 45 and 157
The least common multiple (LCM) of 45 and 157 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 45 and 157?
First, calculate the GCD of 45 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 157 = 0 remainder 45 |
| 2 | 157 ÷ 45 = 3 remainder 22 |
| 3 | 45 ÷ 22 = 2 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 91 | 10010 |
| 183 and 36 | 2196 |
| 13 and 48 | 624 |
| 117 and 30 | 1170 |
| 112 and 120 | 1680 |