Least Common Multiple (LCM) of 45 and 149
The least common multiple (LCM) of 45 and 149 is 6705.
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 149?
First, calculate the GCD of 45 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 149 = 0 remainder 45 |
| 2 | 149 ÷ 45 = 3 remainder 14 |
| 3 | 45 ÷ 14 = 3 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 155 | 19685 |
| 171 and 135 | 2565 |
| 90 and 35 | 630 |
| 196 and 158 | 15484 |
| 157 and 92 | 14444 |