Least Common Multiple (LCM) of 50 and 70
The least common multiple (LCM) of 50 and 70 is 350.
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 50 and 70?
First, calculate the GCD of 50 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 70 = 0 remainder 50 |
| 2 | 70 ÷ 50 = 1 remainder 20 |
| 3 | 50 ÷ 20 = 2 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 116 | 3828 |
| 66 and 79 | 5214 |
| 126 and 147 | 882 |
| 129 and 128 | 16512 |
| 149 and 68 | 10132 |