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46.
Which number is a multiple of all the three
numbers 4, 8 and 6 ?
(A) 396
(B) 664
(C) 696
(D) 5432
47.
What is the largest number which divides 270
and 426, leaving remainder 6 in each case ?
(A) 12
(B) 22
(C) 30
(D) 36
Answers
Answer:
a 369 b 36 is the answer of these
Answer Q. 46:
Concept:
The multiples are the product of any given number multiplied by any other number, the product is known as the multiple of a given number.
Given:
The three numbers are 4, 8, and 6.
To find:
Which one is the multiple in the given options?
Solution:
The LCM of the numbers 4, 8, and 6 is 24.
The prime factorization of 24 is 2²× 3².
The number which contains the term 2²× 3² in its prime factorization will be the multiple of all the three numbers.
The prime factorization of 396 is 2²× 3² × 11.
The prime factorization of 664 is 2³× 83.
The prime factorization of 696 is 2²× 3 × 29.
The prime factorization of 5432 is 2³ × 7× 97
As the term 396 contains 2²× 3², it is the multiple of 4, 8, and 6.
Hence, the correct option is (a) 396.
Answer Q. 47:
Concept:
The greatest number divided by each of the two or more numbers is known as Highest Common Factor (HCF).
Given:
The two numbers are 270 and 426.
To find:
Which one of the given options gives the remainder as 6?
Solution:
Subtracting the numbers by 6:
270-6=264
426-6=420
The numbers are subtracted by 6 as it gives a remainder of 6.
The prime factorization of 264 is 2²× 3 × 11.
The prime factorization of 420 is 2² × 3 × 5 × 7.
Now, calculating the HCF of 264 and 420 which is 12.
So, the largest number which divides 270 and 426, leaving the remainder 6 in each case will be 12.
Hence, the correct option is (a) 12.
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