Least Common Multiple (LCM) of 49 and 140
The least common multiple (LCM) of 49 and 140 is 980.
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 49 and 140?
First, calculate the GCD of 49 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 140 = 0 remainder 49 |
| 2 | 140 ÷ 49 = 2 remainder 42 |
| 3 | 49 ÷ 42 = 1 remainder 7 |
| 4 | 42 ÷ 7 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 60 | 3420 |
| 149 and 109 | 16241 |
| 101 and 105 | 10605 |
| 86 and 169 | 14534 |
| 30 and 131 | 3930 |