Least Common Multiple (LCM) of 35 and 49
The least common multiple (LCM) of 35 and 49 is 245.
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 35 and 49?
First, calculate the GCD of 35 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 49 = 0 remainder 35 |
| 2 | 49 ÷ 35 = 1 remainder 14 |
| 3 | 35 ÷ 14 = 2 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 19 | 2128 |
| 107 and 36 | 3852 |
| 108 and 39 | 1404 |
| 137 and 152 | 20824 |
| 192 and 77 | 14784 |