Least Common Multiple (LCM) of 12 and 72
The least common multiple (LCM) of 12 and 72 is 72.
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 12 and 72?
First, calculate the GCD of 12 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 72 = 0 remainder 12 |
| 2 | 72 ÷ 12 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 74 | 2516 |
| 167 and 29 | 4843 |
| 72 and 111 | 2664 |
| 164 and 91 | 14924 |
| 114 and 188 | 10716 |