Least Common Multiple (LCM) of 21 and 40
The least common multiple (LCM) of 21 and 40 is 840.
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 40?
First, calculate the GCD of 21 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 40 = 0 remainder 21 |
| 2 | 40 ÷ 21 = 1 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 120 | 2040 |
| 103 and 52 | 5356 |
| 125 and 30 | 750 |
| 53 and 22 | 1166 |
| 170 and 46 | 3910 |