Least Common Multiple (LCM) of 45 and 158
The least common multiple (LCM) of 45 and 158 is 7110.
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 158?
First, calculate the GCD of 45 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 158 = 0 remainder 45 |
| 2 | 158 ÷ 45 = 3 remainder 23 |
| 3 | 45 ÷ 23 = 1 remainder 22 |
| 4 | 23 ÷ 22 = 1 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 194 | 2134 |
| 48 and 54 | 432 |
| 106 and 12 | 636 |
| 139 and 20 | 2780 |
| 75 and 147 | 3675 |