Least Common Multiple (LCM) of 103 and 132
The least common multiple (LCM) of 103 and 132 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 103 and 132?
First, calculate the GCD of 103 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 132 = 0 remainder 103 |
| 2 | 132 ÷ 103 = 1 remainder 29 |
| 3 | 103 ÷ 29 = 3 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 114 | 2280 |
| 152 and 87 | 13224 |
| 104 and 149 | 15496 |
| 50 and 72 | 1800 |
| 124 and 109 | 13516 |