Least Common Multiple (LCM) of 35 and 68
The least common multiple (LCM) of 35 and 68 is 2380.
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 68?
First, calculate the GCD of 35 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 68 = 0 remainder 35 |
| 2 | 68 ÷ 35 = 1 remainder 33 |
| 3 | 35 ÷ 33 = 1 remainder 2 |
| 4 | 33 ÷ 2 = 16 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 26 | 3146 |
| 137 and 48 | 6576 |
| 72 and 80 | 720 |
| 149 and 75 | 11175 |
| 52 and 104 | 104 |