Least Common Multiple (LCM) of 21 and 181
The least common multiple (LCM) of 21 and 181 is 3801.
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 181?
First, calculate the GCD of 21 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 181 = 0 remainder 21 |
| 2 | 181 ÷ 21 = 8 remainder 13 |
| 3 | 21 ÷ 13 = 1 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 185 | 13135 |
| 144 and 38 | 2736 |
| 65 and 134 | 8710 |
| 134 and 42 | 2814 |
| 120 and 112 | 1680 |