Least Common Multiple (LCM) of 113 and 63
The least common multiple (LCM) of 113 and 63 is 7119.
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 63?
First, calculate the GCD of 113 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 63 = 1 remainder 50 |
| 2 | 63 ÷ 50 = 1 remainder 13 |
| 3 | 50 ÷ 13 = 3 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 129 | 10320 |
| 168 and 124 | 5208 |
| 140 and 42 | 420 |
| 24 and 47 | 1128 |
| 59 and 67 | 3953 |