Least Common Multiple (LCM) of 116 and 63
The least common multiple (LCM) of 116 and 63 is 7308.
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 116 and 63?
First, calculate the GCD of 116 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 63 = 1 remainder 53 |
| 2 | 63 ÷ 53 = 1 remainder 10 |
| 3 | 53 ÷ 10 = 5 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 130 | 1170 |
| 69 and 189 | 4347 |
| 104 and 103 | 10712 |
| 59 and 129 | 7611 |
| 53 and 74 | 3922 |