Least Common Multiple (LCM) of 112 and 35
The least common multiple (LCM) of 112 and 35 is 560.
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 35?
First, calculate the GCD of 112 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 35 = 3 remainder 7 |
| 2 | 35 ÷ 7 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 98 | 17542 |
| 65 and 97 | 6305 |
| 141 and 174 | 8178 |
| 57 and 81 | 1539 |
| 144 and 63 | 1008 |