Least Common Multiple (LCM) of 112 and 49
The least common multiple (LCM) of 112 and 49 is 784.
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 112 and 49?
First, calculate the GCD of 112 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 49 = 2 remainder 14 |
| 2 | 49 ÷ 14 = 3 remainder 7 |
| 3 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 51 | 714 |
| 84 and 175 | 2100 |
| 65 and 182 | 910 |
| 167 and 61 | 10187 |
| 70 and 150 | 1050 |