Find the least number divisible by each natural number less than or equal to 10.
These are the possible answers
A) 100 B) 3,628,800 C) 2520 D) 30,240
I don't understand this question at all. Do you?
2
3
2x2
5
2x3
7
2x2x2
3x3
2x5
so we need 2x2x2x3x3x5x7 = 504
This is just like finding the LCD for
1 + 1/2 + 1/3 + ... + 19 + 110
I see what you are saying, and thank you for trying to explain. What I am confused about is none of the answers anyone has given me is a possible answer in my multiple choice options.
A) 100
b) 3,628,800
c) 2520
d) 30,240
You breaking it down as the LCD has made the most sense. But do you see the dilema with the choice options?
Thanks, the product of my factors is <b.2520 , and not 504
I must have missed the 5 in my multiplication.
Sorry about the silly arithmetic error, amazing how we all depend on our calculators
Thanks, the product of my factors is 2520 , and not 504
I must have missed the 5 in my multiplication.
Sorry about the silly arithmetic error, amazing how we all depend on our calculators
No worries. I appreciate your help and explanation. Thank you!
To find the least number that is divisible by each natural number less than or equal to 10, we can use the concept of the least common multiple (LCM). The LCM of a set of numbers is the smallest number that is evenly divisible by all the numbers in the set.
To find the LCM in this case, we need to list the prime factors of each number from 1 to 10:
1 = 1 (Prime factorization: 1)
2 = 2 (Prime factorization: 2)
3 = 3 (Prime factorization: 3)
4 = 2 * 2 (Prime factorization: 2^2)
5 = 5 (Prime factorization: 5)
6 = 2 * 3 (Prime factorization: 2 * 3)
7 = 7 (Prime factorization: 7)
8 = 2 * 2 * 2 (Prime factorization: 2^3)
9 = 3 * 3 (Prime factorization: 3^2)
10 = 2 * 5 (Prime factorization: 2 * 5)
To find the LCM, we take the highest power of each prime factor:
2^3 * 3^2 * 5 * 7 = 2 * 2 * 2 * 3 * 3 * 5 * 7 = 2,520
Therefore, the least number divisible by each natural number less than or equal to 10 is 2,520.