Least Common Multiple (LCM) of 21 and 131
The least common multiple (LCM) of 21 and 131 is 2751.
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 131?
First, calculate the GCD of 21 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 131 = 0 remainder 21 |
| 2 | 131 ÷ 21 = 6 remainder 5 |
| 3 | 21 ÷ 5 = 4 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 89 | 12549 |
| 158 and 150 | 11850 |
| 195 and 95 | 3705 |
| 71 and 185 | 13135 |
| 112 and 24 | 336 |