Least Common Multiple (LCM) of 21 and 100
The least common multiple (LCM) of 21 and 100 is 2100.
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 21 and 100?
First, calculate the GCD of 21 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 100 = 0 remainder 21 |
| 2 | 100 ÷ 21 = 4 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 47 | 1457 |
| 21 and 185 | 3885 |
| 64 and 198 | 6336 |
| 79 and 155 | 12245 |
| 30 and 42 | 210 |