Least Common Multiple (LCM) of 16 and 68
The least common multiple (LCM) of 16 and 68 is 272.
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 16 and 68?
First, calculate the GCD of 16 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 68 = 0 remainder 16 |
| 2 | 68 ÷ 16 = 4 remainder 4 |
| 3 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 124 | 7316 |
| 110 and 133 | 14630 |
| 165 and 39 | 2145 |
| 152 and 87 | 13224 |
| 70 and 175 | 350 |