What is the least common multiple of set of numbers? 3,10,12,8
Start with the largest number -- 12
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180 . . .
Which of the above numbers is evenly divisible by 3, 10, and 8?
120
3= 3
10 = 2*5
12 = 2*2*3
8 = 2*2*2
start with the longest string of prime factors : 2*2*2
now add on any other factors from the other strings that have not yet been put down
2*2*2*3*5 = 120
To find the least common multiple (LCM) of a set of numbers, you can follow these steps:
Step 1: Find the prime factorization of each number in the set.
Let's start with the numbers 3, 10, 12, and 8:
- 3 is already a prime number.
- 10 can be written as 2 × 5.
- 12 can be written as 2² × 3.
- 8 can be written as 2³.
Step 2: Write down the highest power of each unique prime factor.
From the prime factorization, list down the prime factors with their highest exponent:
- 2³: The highest power of 2 in the set is 2³.
- 3: There is only one prime factor 3 in the set.
- 5: There is only one prime factor 5 in the set.
Step 3: Multiply all the prime factors obtained in Step 2.
Multiply the prime factors obtained in Step 2:
2³ × 3 × 5 = 120
Therefore, the least common multiple (LCM) of the numbers 3, 10, 12, and 8 is 120.