Least Common Multiple (LCM) of 21 and 141
The least common multiple (LCM) of 21 and 141 is 987.
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 141?
First, calculate the GCD of 21 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 141 = 0 remainder 21 |
| 2 | 141 ÷ 21 = 6 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 129 | 5289 |
| 36 and 107 | 3852 |
| 175 and 172 | 30100 |
| 83 and 152 | 12616 |
| 15 and 199 | 2985 |