Least Common Multiple (LCM) of 43 and 35
The least common multiple (LCM) of 43 and 35 is 1505.
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 43 and 35?
First, calculate the GCD of 43 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 35 = 1 remainder 8 |
| 2 | 35 ÷ 8 = 4 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 15 | 1560 |
| 93 and 13 | 1209 |
| 27 and 141 | 1269 |
| 82 and 116 | 4756 |
| 113 and 98 | 11074 |