Least Common Multiple (LCM) of 101 and 63
The least common multiple (LCM) of 101 and 63 is 6363.
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 101 and 63?
First, calculate the GCD of 101 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 63 = 1 remainder 38 |
| 2 | 63 ÷ 38 = 1 remainder 25 |
| 3 | 38 ÷ 25 = 1 remainder 13 |
| 4 | 25 ÷ 13 = 1 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 134 | 6432 |
| 41 and 127 | 5207 |
| 86 and 74 | 3182 |
| 134 and 84 | 5628 |
| 137 and 125 | 17125 |