Least Common Multiple (LCM) of 72 and 188
The least common multiple (LCM) of 72 and 188 is 3384.
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 72 and 188?
First, calculate the GCD of 72 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 188 = 0 remainder 72 |
| 2 | 188 ÷ 72 = 2 remainder 44 |
| 3 | 72 ÷ 44 = 1 remainder 28 |
| 4 | 44 ÷ 28 = 1 remainder 16 |
| 5 | 28 ÷ 16 = 1 remainder 12 |
| 6 | 16 ÷ 12 = 1 remainder 4 |
| 7 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 31 | 4216 |
| 112 and 101 | 11312 |
| 128 and 150 | 9600 |
| 163 and 79 | 12877 |
| 22 and 137 | 3014 |