Least Common Multiple (LCM) of 132 and 149
The least common multiple (LCM) of 132 and 149 is 19668.
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 132 and 149?
First, calculate the GCD of 132 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 149 = 0 remainder 132 |
| 2 | 149 ÷ 132 = 1 remainder 17 |
| 3 | 132 ÷ 17 = 7 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 165 | 2805 |
| 123 and 169 | 20787 |
| 145 and 189 | 27405 |
| 72 and 89 | 6408 |
| 38 and 54 | 1026 |