Least Common Multiple (LCM) of 172 and 20
The least common multiple (LCM) of 172 and 20 is 860.
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 172 and 20?
First, calculate the GCD of 172 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 20 = 8 remainder 12 |
| 2 | 20 ÷ 12 = 1 remainder 8 |
| 3 | 12 ÷ 8 = 1 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 186 | 13206 |
| 112 and 123 | 13776 |
| 100 and 122 | 6100 |
| 101 and 195 | 19695 |
| 105 and 80 | 1680 |