Least Common Multiple (LCM) of 77 and 170
The least common multiple (LCM) of 77 and 170 is 13090.
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 77 and 170?
First, calculate the GCD of 77 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 170 = 0 remainder 77 |
| 2 | 170 ÷ 77 = 2 remainder 16 |
| 3 | 77 ÷ 16 = 4 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 190 | 15770 |
| 17 and 99 | 1683 |
| 35 and 114 | 3990 |
| 135 and 137 | 18495 |
| 107 and 45 | 4815 |