Least Common Multiple (LCM) of 107 and 132
The least common multiple (LCM) of 107 and 132 is 14124.
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 107 and 132?
First, calculate the GCD of 107 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 132 = 0 remainder 107 |
| 2 | 132 ÷ 107 = 1 remainder 25 |
| 3 | 107 ÷ 25 = 4 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 90 | 9270 |
| 85 and 52 | 4420 |
| 167 and 102 | 17034 |
| 35 and 131 | 4585 |
| 175 and 88 | 15400 |