Least Common Multiple (LCM) of 163 and 21
The least common multiple (LCM) of 163 and 21 is 3423.
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 163 and 21?
First, calculate the GCD of 163 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 21 = 7 remainder 16 |
| 2 | 21 ÷ 16 = 1 remainder 5 |
| 3 | 16 ÷ 5 = 3 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 31 | 5425 |
| 129 and 190 | 24510 |
| 105 and 103 | 10815 |
| 63 and 54 | 378 |
| 89 and 72 | 6408 |