Least Common Multiple (LCM) of 61 and 170
The least common multiple (LCM) of 61 and 170 is 10370.
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 61 and 170?
First, calculate the GCD of 61 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 170 = 0 remainder 61 |
| 2 | 170 ÷ 61 = 2 remainder 48 |
| 3 | 61 ÷ 48 = 1 remainder 13 |
| 4 | 48 ÷ 13 = 3 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 134 | 8710 |
| 16 and 103 | 1648 |
| 88 and 67 | 5896 |
| 186 and 200 | 18600 |
| 101 and 128 | 12928 |