pls ans with explaination or I will report your account
Answers
Answer:
Required number is 997920
Step-by-step explanation:
Given numbers are 27 , 45 , 60 , 72 and 96
We have to find greatest 6-digit number which is divisible by given numbers.
We first find lowest Common Multiple of given numbers then we find multiple of LCM which greatest 6 digit number.
27 = 3 × 3 × 3
45 = 5 × 3 × 3
60 = 2 × 3 × 2 × 5
72 = 2 × 2 × 2 × 3 × 3
96 = 2 × 2 × 2 × 2 × 2 × 3
LCM = 3 × 3 × 2 × 2 × 2 × 2 × 2 × 3 × 5 = 4320
Now we find the multiples of 4320 which is largest 6 digit number
for divide 999999 ÷ 4320 we get 231.48125
So, 231st multiple of 4320 is largest 6 digit number .i.e., 4320 × 231 = 997920
Therefore, required number is 997920
least number
Let's break all those down into prime factors:
27 = 3*3*3
45 = 3*3*5
60 = 2*2*3*5
72 = 2*2*2*3*3
96 = 2*2*2*2*2*3
Let's check to see which of those has the most 2 factors:
27 has 0 2's
45 has 0 2's
60 has 2 2's
72 has 3 2's
96 has 5 2's
The most in that list is 5 2's. So the LCM has 5 2's
27 = 3*3*3
45 = 3*3*5
60 = 2*2*3*5
72 = 2*2*2*3*3
96 = 2*2*2*2*2*3
Let's check to see which of those has the most 3 factors:
27 has 3 3's
45 has 2 3's
60 has 1 3
72 has 2 3's
96 has 1 3's
The most in that list is 3 3's. So the LCM has 5 2's and 3 3's
27 = 3*3*3
45 = 3*3*5
60 = 2*2*3*5
72 = 2*2*2*3*3
96 = 2*2*2*2*2*3
Let's check to see which of those has the most 5 factors:
27 has 0 5's
45 has 1 5
60 has 1 5
72 has 0 5's
96 has 0 5's
The most on that list is 1 5. So the LCM has 5 2's, 3 3's, and 1 5.
So LCM = 2*2*2*2*2*3*3*3*5 = 4320