Least Common Multiple (LCM) of 113 and 77
The least common multiple (LCM) of 113 and 77 is 8701.
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 77?
First, calculate the GCD of 113 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 77 = 1 remainder 36 |
| 2 | 77 ÷ 36 = 2 remainder 5 |
| 3 | 36 ÷ 5 = 7 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 195 | 195 |
| 24 and 157 | 3768 |
| 138 and 122 | 8418 |
| 66 and 115 | 7590 |
| 52 and 53 | 2756 |