Least Common Multiple (LCM) of 72 and 170
The least common multiple (LCM) of 72 and 170 is 6120.
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 72 and 170?
First, calculate the GCD of 72 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 170 = 0 remainder 72 |
| 2 | 170 ÷ 72 = 2 remainder 26 |
| 3 | 72 ÷ 26 = 2 remainder 20 |
| 4 | 26 ÷ 20 = 1 remainder 6 |
| 5 | 20 ÷ 6 = 3 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 109 | 11227 |
| 97 and 175 | 16975 |
| 48 and 117 | 1872 |
| 106 and 18 | 954 |
| 187 and 196 | 36652 |