Least Common Multiple (LCM) of 63 and 113
The least common multiple (LCM) of 63 and 113 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 63 and 113?
First, calculate the GCD of 63 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 113 = 0 remainder 63 |
| 2 | 113 ÷ 63 = 1 remainder 50 |
| 3 | 63 ÷ 50 = 1 remainder 13 |
| 4 | 50 ÷ 13 = 3 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 178 | 3382 |
| 119 and 63 | 1071 |
| 172 and 15 | 2580 |
| 147 and 160 | 23520 |
| 190 and 134 | 12730 |