Least Common Multiple (LCM) of 35 and 102
The least common multiple (LCM) of 35 and 102 is 3570.
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 102?
First, calculate the GCD of 35 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 102 = 0 remainder 35 |
| 2 | 102 ÷ 35 = 2 remainder 32 |
| 3 | 35 ÷ 32 = 1 remainder 3 |
| 4 | 32 ÷ 3 = 10 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 186 | 6324 |
| 165 and 137 | 22605 |
| 84 and 72 | 504 |
| 108 and 77 | 8316 |
| 33 and 121 | 363 |