Least Common Multiple (LCM) of 170 and 61
The least common multiple (LCM) of 170 and 61 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 170 and 61?
First, calculate the GCD of 170 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 61 = 2 remainder 48 |
| 2 | 61 ÷ 48 = 1 remainder 13 |
| 3 | 48 ÷ 13 = 3 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 12 | 132 |
| 16 and 107 | 1712 |
| 31 and 113 | 3503 |
| 145 and 200 | 5800 |
| 155 and 56 | 8680 |