Least Common Multiple (LCM) of 63 and 102
The least common multiple (LCM) of 63 and 102 is 2142.
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 102?
First, calculate the GCD of 63 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 102 = 0 remainder 63 |
| 2 | 102 ÷ 63 = 1 remainder 39 |
| 3 | 63 ÷ 39 = 1 remainder 24 |
| 4 | 39 ÷ 24 = 1 remainder 15 |
| 5 | 24 ÷ 15 = 1 remainder 9 |
| 6 | 15 ÷ 9 = 1 remainder 6 |
| 7 | 9 ÷ 6 = 1 remainder 3 |
| 8 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 179 | 33115 |
| 200 and 28 | 1400 |
| 165 and 171 | 9405 |
| 90 and 24 | 360 |
| 154 and 97 | 14938 |