Least Common Multiple (LCM) of 21 and 173
The least common multiple (LCM) of 21 and 173 is 3633.
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 173?
First, calculate the GCD of 21 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 173 = 0 remainder 21 |
| 2 | 173 ÷ 21 = 8 remainder 5 |
| 3 | 21 ÷ 5 = 4 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 74 | 5180 |
| 39 and 60 | 780 |
| 146 and 90 | 6570 |
| 118 and 22 | 1298 |
| 166 and 105 | 17430 |