Least Common Multiple (LCM) of 35 and 170
The least common multiple (LCM) of 35 and 170 is 1190.
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 35 and 170?
First, calculate the GCD of 35 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 170 = 0 remainder 35 |
| 2 | 170 ÷ 35 = 4 remainder 30 |
| 3 | 35 ÷ 30 = 1 remainder 5 |
| 4 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 105 | 7455 |
| 161 and 53 | 8533 |
| 135 and 36 | 540 |
| 124 and 194 | 12028 |
| 111 and 11 | 1221 |