Least Common Multiple (LCM) of 21 and 101
The least common multiple (LCM) of 21 and 101 is 2121.
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 101?
First, calculate the GCD of 21 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 101 = 0 remainder 21 |
| 2 | 101 ÷ 21 = 4 remainder 17 |
| 3 | 21 ÷ 17 = 1 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 190 | 13110 |
| 82 and 35 | 2870 |
| 169 and 116 | 19604 |
| 106 and 161 | 17066 |
| 186 and 184 | 17112 |