Least Common Multiple (LCM) of 101 and 21
The least common multiple (LCM) of 101 and 21 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 101 and 21?
First, calculate the GCD of 101 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 21 = 4 remainder 17 |
| 2 | 21 ÷ 17 = 1 remainder 4 |
| 3 | 17 ÷ 4 = 4 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 14 | 2226 |
| 106 and 50 | 2650 |
| 172 and 129 | 516 |
| 139 and 78 | 10842 |
| 73 and 133 | 9709 |