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Introduction to Divisibility and Its Meaning

L.C.M of the ...

Question

L.C.M of the $1$ and the two-digit natural number is ………….. .

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Solution

As we know that smallest natural number is $1$ and the two-digit natural number is $10 .$
Multiples of $1 = 1, 2, 3, 4, 5, 6, . . . . . . . . . . . . .$
Multiples of $10 = 10, 20, 30, 40, 50, 60, . . . . . . . . . . . . . . . .$
L.C.M $(1, 10) = 10$
Hence, the least common multiple of the smallest natural and the smallest prime number is $10 .$

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Q. Which of the following statements are true and which are false?

(i) Every whole number has its successor.
(ii) Every whole number has its predecessor.
(iii) 0 is the smallest natural number.
(iv) 1 is the smallest whole number.
(v) 0 is less than every natural number.
(vi) Between any two whole numbers there is a whole number.
(vii) Between any two non-consecutive whole numbers there is a whole number.
(viii) The smallest 5-digit number is the successor of the largest 4 digit number
(ix) Of the given two natural numbers, the one having more digits is greater.
(x) The predecessor of a two digit number cannot be a single digit number.
(xi) If a and b are natural numbers and a < b, than there is a natural number c such that a<b<c.
(xii) If a and b are whole numbers and a<b, then a+1< b+1.
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(xiv) The natural number 1 has no predecessor.

Q. Write (T) for true and (F) for false against each of the following statements:
(i) Zero is the smallest natural number.
(ii) Zero is the smallest whole number.
(iii) Every whole number is a natural number.
(iv) Every natural number is a whole number.
(v) 1 is the smallest whole number.
(vi) The natural number 1 has no predecessor.
(vii) The whole number 1 has no predecessor.
(viii) The whole number 0 has no predecessor.
(ix) The predecessor of a two-digit number is never a single-digit number.
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(xii) 7000 is the successor of 6999.

Q. The sum of the squares of the LCM and the GCD of two natural numbers is 2308. If the product of the two natural numbers is 96, what could the sum of their LCM and GCD be?

The LCM of the smallest two-digit composite number and the smallest composite number is :

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