Least Common Multiple (LCM) of 10 and 49
The least common multiple (LCM) of 10 and 49 is 490.
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 10 and 49?
First, calculate the GCD of 10 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 49 = 0 remainder 10 |
| 2 | 49 ÷ 10 = 4 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 100 | 700 |
| 193 and 40 | 7720 |
| 164 and 23 | 3772 |
| 108 and 44 | 1188 |
| 68 and 173 | 11764 |