Least Common Multiple (LCM) of 102 and 132
The least common multiple (LCM) of 102 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 102 and 132?
First, calculate the GCD of 102 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 132 = 0 remainder 102 |
| 2 | 132 ÷ 102 = 1 remainder 30 |
| 3 | 102 ÷ 30 = 3 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 188 | 5076 |
| 40 and 59 | 2360 |
| 131 and 127 | 16637 |
| 190 and 173 | 32870 |
| 110 and 139 | 15290 |