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 |
|---|---|
| 137 and 134 | 18358 |
| 67 and 191 | 12797 |
| 17 and 33 | 561 |
| 138 and 85 | 11730 |
| 150 and 48 | 1200 |