Short Answer TypeFind the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (ii) 510 and 92
Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (iii) 336 and 54
Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21
Find the LCM and HCF of the following integers by applying the prime factorisation method. (ii) 17, 23 and 29
Find the LCM and HCF of the following integers by applying the prime factorisation method. (iii) 8, 9 and 25
Check whether 6n can end with the digit 0 for any natural number n
If the number 6n, for any natural number n, ends with digit 0, then it is divisible by 5. That is, the prime factorisation of 6n contains the prime 5. This is not possible because the primes in the factorisation of 6n are 2 and 3 and the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorisation of 6n.
So, there is no natural number n for which 6n ends with digit zero.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
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