Least Common Multiple (LCM) of 70 and 43
The least common multiple (LCM) of 70 and 43 is 3010.
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 70 and 43?
First, calculate the GCD of 70 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 43 = 1 remainder 27 |
| 2 | 43 ÷ 27 = 1 remainder 16 |
| 3 | 27 ÷ 16 = 1 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 117 | 3744 |
| 45 and 154 | 6930 |
| 135 and 118 | 15930 |
| 99 and 56 | 5544 |
| 193 and 40 | 7720 |