Least Common Multiple (LCM) of 113 and 132
The least common multiple (LCM) of 113 and 132 is 14916.
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 113 and 132?
First, calculate the GCD of 113 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 132 = 0 remainder 113 |
| 2 | 132 ÷ 113 = 1 remainder 19 |
| 3 | 113 ÷ 19 = 5 remainder 18 |
| 4 | 19 ÷ 18 = 1 remainder 1 |
| 5 | 18 ÷ 1 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 160 | 160 |
| 152 and 166 | 12616 |
| 22 and 105 | 2310 |
| 112 and 181 | 20272 |
| 21 and 73 | 1533 |