Least Common Multiple (LCM) of 13 and 118
The least common multiple (LCM) of 13 and 118 is 1534.
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 118?
First, calculate the GCD of 13 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 118 = 0 remainder 13 |
| 2 | 118 ÷ 13 = 9 remainder 1 |
| 3 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 109 | 11445 |
| 90 and 19 | 1710 |
| 138 and 81 | 3726 |
| 166 and 34 | 2822 |
| 171 and 64 | 10944 |