Least Common Multiple (LCM) of 138 and 116
The least common multiple (LCM) of 138 and 116 is 8004.
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 138 and 116?
First, calculate the GCD of 138 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 116 = 1 remainder 22 |
| 2 | 116 ÷ 22 = 5 remainder 6 |
| 3 | 22 ÷ 6 = 3 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 93 | 4464 |
| 115 and 16 | 1840 |
| 199 and 91 | 18109 |
| 32 and 171 | 5472 |
| 58 and 113 | 6554 |