Least Common Multiple (LCM) of 21 and 107
The least common multiple (LCM) of 21 and 107 is 2247.
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 107?
First, calculate the GCD of 21 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 107 = 0 remainder 21 |
| 2 | 107 ÷ 21 = 5 remainder 2 |
| 3 | 21 ÷ 2 = 10 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 64 | 1728 |
| 188 and 118 | 11092 |
| 136 and 67 | 9112 |
| 164 and 161 | 26404 |
| 164 and 21 | 3444 |