Least Common Multiple (LCM) of 100 and 63
The least common multiple (LCM) of 100 and 63 is 6300.
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 100 and 63?
First, calculate the GCD of 100 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 63 = 1 remainder 37 |
| 2 | 63 ÷ 37 = 1 remainder 26 |
| 3 | 37 ÷ 26 = 1 remainder 11 |
| 4 | 26 ÷ 11 = 2 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 56 | 1400 |
| 134 and 152 | 10184 |
| 55 and 117 | 6435 |
| 20 and 79 | 1580 |
| 126 and 82 | 5166 |