Least Common Multiple (LCM) of 21 and 85
The least common multiple (LCM) of 21 and 85 is 1785.
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 85?
First, calculate the GCD of 21 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 85 = 0 remainder 21 |
| 2 | 85 ÷ 21 = 4 remainder 1 |
| 3 | 21 ÷ 1 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 44 | 4620 |
| 68 and 164 | 2788 |
| 157 and 64 | 10048 |
| 10 and 90 | 90 |
| 40 and 91 | 3640 |