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primary 6 | Maths
| Data Analysis
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Date Posted: 4 years ago
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a,b,c are 3,7,11. 2020 is already divisible by 5. in order 2020abc divisible by 3,7,11 as well require to multiply them in.
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Can u show me the working
The question is testing on Lowest Common Multiple (LCM). It’s more of a theory than showing of workings.
For any number (other than prime), there will be factors; numbers that when multiplied together gives the original number.
That being said, if you divide a number (eg 6) with another (eg 2) and gives no remainder, the second number (eg 2) is said to be a factor.
Similarly in 2020, 5 is a factor of said number. 3,7,11 are not.
For 2020abc to be divisible by 3,5,7,11, you need to consider only 3,7,11 as factors to give you a LCM since 2020 is as previously mentioned, divisible by 5 already.
For any number (other than prime), there will be factors; numbers that when multiplied together gives the original number.
That being said, if you divide a number (eg 6) with another (eg 2) and gives no remainder, the second number (eg 2) is said to be a factor.
Similarly in 2020, 5 is a factor of said number. 3,7,11 are not.
For 2020abc to be divisible by 3,5,7,11, you need to consider only 3,7,11 as factors to give you a LCM since 2020 is as previously mentioned, divisible by 5 already.
2020 ÷ 2 = 1010
1010 ÷ 2 = 505
505 ÷ 5 = 101
101 is a prime number and cannot be divided exactly by any whole number to give another whole number, except by 1 or itself.
Therefore 2020 = 101 x 5 x 2 x 2
Then 2020abc = 101 x 5 x 2 x 2 x a x b x c
There is a factor of 5 in 2020 so it's a multiple of 5 and thus exactly divisible by 5.
But as there are no factors of 3, 7 and 11 in the number 2020, it is not a multiple of these factors. So 2020 isn't exactly divisible by 3, 7 or 11.
However, multiplying 2020 by 3, 7 or 11 makes it exactly divisible by each said factor respectively. So we do all three and multiply the number 2020 by 3, 7 and 11.
3,5,7 and 11 are prime numbers/factors and cannot be broken up into more factors, except itself and 1.
So we don't have to multiply 2020 by anything bigger that those since we want the smallest a,b and c, which in turn gives the smallest 2020abc.
Therefore we can let 2020abc be 2020 x 3 x 7 x 11.
Your a,b and c are 3,7,11.
Notice that it doesn't matter which is which since a,b,c are just alphabets that represent a number each.
Eg. you can have :
a = 3,b = 7, c = 11 or
a = 3, b = 11, c = 7 or
a = 7, b = 3, c = 11 or
a = 7, b = 11, c = 3 or
a = 11, b = 3, c = 7 or
a = 11, b = 7, c = 3
Choosing any one of these 6 options will still give you a result that is divisible by 3,5,7,11
1010 ÷ 2 = 505
505 ÷ 5 = 101
101 is a prime number and cannot be divided exactly by any whole number to give another whole number, except by 1 or itself.
Therefore 2020 = 101 x 5 x 2 x 2
Then 2020abc = 101 x 5 x 2 x 2 x a x b x c
There is a factor of 5 in 2020 so it's a multiple of 5 and thus exactly divisible by 5.
But as there are no factors of 3, 7 and 11 in the number 2020, it is not a multiple of these factors. So 2020 isn't exactly divisible by 3, 7 or 11.
However, multiplying 2020 by 3, 7 or 11 makes it exactly divisible by each said factor respectively. So we do all three and multiply the number 2020 by 3, 7 and 11.
3,5,7 and 11 are prime numbers/factors and cannot be broken up into more factors, except itself and 1.
So we don't have to multiply 2020 by anything bigger that those since we want the smallest a,b and c, which in turn gives the smallest 2020abc.
Therefore we can let 2020abc be 2020 x 3 x 7 x 11.
Your a,b and c are 3,7,11.
Notice that it doesn't matter which is which since a,b,c are just alphabets that represent a number each.
Eg. you can have :
a = 3,b = 7, c = 11 or
a = 3, b = 11, c = 7 or
a = 7, b = 3, c = 11 or
a = 7, b = 11, c = 3 or
a = 11, b = 3, c = 7 or
a = 11, b = 7, c = 3
Choosing any one of these 6 options will still give you a result that is divisible by 3,5,7,11
See 1 Answer
a,b,c are 3,7,11. 2020 is already divisible by 5. in order 2020abc divisible by 3,7,11 as well require to multiply them in. 3,7,11 are prime numbers as well.
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