Least Common Multiple (LCM) of 120 and 147
The least common multiple (LCM) of 120 and 147 is 5880.
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 120 and 147?
First, calculate the GCD of 120 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 147 = 0 remainder 120 |
| 2 | 147 ÷ 120 = 1 remainder 27 |
| 3 | 120 ÷ 27 = 4 remainder 12 |
| 4 | 27 ÷ 12 = 2 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 55 | 5885 |
| 111 and 70 | 7770 |
| 38 and 118 | 2242 |
| 53 and 134 | 7102 |
| 105 and 77 | 1155 |