Least Common Multiple (LCM) of 21 and 106
The least common multiple (LCM) of 21 and 106 is 2226.
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 106?
First, calculate the GCD of 21 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 106 = 0 remainder 21 |
| 2 | 106 ÷ 21 = 5 remainder 1 |
| 3 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 57 | 2451 |
| 114 and 15 | 570 |
| 101 and 110 | 11110 |
| 45 and 134 | 6030 |
| 101 and 84 | 8484 |