Least Common Multiple (LCM) of 72 and 120
The least common multiple (LCM) of 72 and 120 is 360.
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 120?
First, calculate the GCD of 72 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 120 = 0 remainder 72 |
| 2 | 120 ÷ 72 = 1 remainder 48 |
| 3 | 72 ÷ 48 = 1 remainder 24 |
| 4 | 48 ÷ 24 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 74 | 4810 |
| 42 and 157 | 6594 |
| 156 and 85 | 13260 |
| 109 and 192 | 20928 |
| 159 and 32 | 5088 |