Least Common Multiple (LCM) of 63 and 118
The least common multiple (LCM) of 63 and 118 is 7434.
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 118?
First, calculate the GCD of 63 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 118 = 0 remainder 63 |
| 2 | 118 ÷ 63 = 1 remainder 55 |
| 3 | 63 ÷ 55 = 1 remainder 8 |
| 4 | 55 ÷ 8 = 6 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 36 | 756 |
| 16 and 133 | 2128 |
| 16 and 115 | 1840 |
| 78 and 171 | 4446 |
| 144 and 140 | 5040 |