Least Common Multiple (LCM) of 17 and 132
The least common multiple (LCM) of 17 and 132 is 2244.
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 17 and 132?
First, calculate the GCD of 17 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 132 = 0 remainder 17 |
| 2 | 132 ÷ 17 = 7 remainder 13 |
| 3 | 17 ÷ 13 = 1 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 157 | 23550 |
| 80 and 68 | 1360 |
| 51 and 99 | 1683 |
| 172 and 63 | 10836 |
| 13 and 51 | 663 |