Least Common Multiple (LCM) of 132 and 172
The least common multiple (LCM) of 132 and 172 is 5676.
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 172?
First, calculate the GCD of 132 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 172 = 0 remainder 132 |
| 2 | 172 ÷ 132 = 1 remainder 40 |
| 3 | 132 ÷ 40 = 3 remainder 12 |
| 4 | 40 ÷ 12 = 3 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 45 | 1530 |
| 44 and 143 | 572 |
| 136 and 104 | 1768 |
| 172 and 26 | 2236 |
| 165 and 125 | 4125 |