Least Common Multiple (LCM) of 102 and 63
The least common multiple (LCM) of 102 and 63 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 102 and 63?
First, calculate the GCD of 102 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 63 = 1 remainder 39 |
| 2 | 63 ÷ 39 = 1 remainder 24 |
| 3 | 39 ÷ 24 = 1 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 93 | 3441 |
| 94 and 57 | 5358 |
| 160 and 157 | 25120 |
| 132 and 92 | 3036 |
| 81 and 81 | 81 |