Least Common Multiple (LCM) of 170 and 72
The least common multiple (LCM) of 170 and 72 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 170 and 72?
First, calculate the GCD of 170 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 72 = 2 remainder 26 |
| 2 | 72 ÷ 26 = 2 remainder 20 |
| 3 | 26 ÷ 20 = 1 remainder 6 |
| 4 | 20 ÷ 6 = 3 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 187 | 25806 |
| 42 and 187 | 7854 |
| 74 and 51 | 3774 |
| 51 and 62 | 3162 |
| 74 and 140 | 5180 |