Least Common Multiple (LCM) of 13 and 114
The least common multiple (LCM) of 13 and 114 is 1482.
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 13 and 114?
First, calculate the GCD of 13 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 114 = 0 remainder 13 |
| 2 | 114 ÷ 13 = 8 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 99 | 4257 |
| 64 and 116 | 1856 |
| 137 and 149 | 20413 |
| 135 and 75 | 675 |
| 50 and 165 | 1650 |