Least Common Multiple (LCM) of 56 and 138
The least common multiple (LCM) of 56 and 138 is 3864.
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 56 and 138?
First, calculate the GCD of 56 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 138 = 0 remainder 56 |
| 2 | 138 ÷ 56 = 2 remainder 26 |
| 3 | 56 ÷ 26 = 2 remainder 4 |
| 4 | 26 ÷ 4 = 6 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 115 | 21735 |
| 119 and 124 | 14756 |
| 184 and 166 | 15272 |
| 144 and 91 | 13104 |
| 79 and 37 | 2923 |