Least Common Multiple (LCM) of 132 and 103
The least common multiple (LCM) of 132 and 103 is 13596.
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 103?
First, calculate the GCD of 132 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 103 = 1 remainder 29 |
| 2 | 103 ÷ 29 = 3 remainder 16 |
| 3 | 29 ÷ 16 = 1 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 41 | 7503 |
| 118 and 130 | 7670 |
| 42 and 65 | 2730 |
| 185 and 135 | 4995 |
| 141 and 52 | 7332 |