Least Common Multiple (LCM) of 112 and 21
The least common multiple (LCM) of 112 and 21 is 336.
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 21?
First, calculate the GCD of 112 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 21 = 5 remainder 7 |
| 2 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 148 | 23532 |
| 175 and 16 | 2800 |
| 147 and 30 | 1470 |
| 167 and 11 | 1837 |
| 163 and 70 | 11410 |