February 14 is celebrated as International Book Giving Day and many countries in the world celebrate this day. Some people in India also started celebrating this day and donated the following number of books of various subjects to a public library : History = 96, Science = 240, Mathematics = 336. These books have to be arranged in minimum number of stacks such that each stack contains books of only one subject and the number of books on each stack is the same.

Assertion (A) : For any two natural numbers a and b, the HCF of a and b is a factor of the LCM of a and b. Reason (R) : HCF of any two natural numbers divides both the numbers.

Assertion-ReasonHCF Using Prime Factorisation MethodRelationship Between HCF and LCM of Two Numbers

State the "Fundamental Theorem of Arithmetic" and use it to find LCM of 36 and 54.

TextFundamental Theorem of ArithmeticLCM Using Prime Factorisation MethodIrrationality of Square Root of Prime Numbers

Show that 45ⁿ can not end with the digit 0, n being a natural number. Write the prime number 'a' which on multiplying with 45ⁿ makes the product end with the digit 0.

TextFundamental Theorem of ArithmeticPrime Factorisation of Natural Numbers

Using prime factorisation, find the HCF of 180, 140 and 210.

TextPrime Factorisation of Natural NumbersHCF Using Prime Factorisation Method