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
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
Any positive number, which has more than two factors, is called a composite number.
Since,
7 × 11 × 13 + 13 = 13 × (7 × 11 + 1)
= 13 × 78
= 13 × 13 × 3 × 2
that is, the given number has more than two factors and it is a composite number.
Similarly,
7 × 6 × 5 × 4 × 3 + 5
= 5 × (7 × 6 × 4 × 3 + 1)
= 5 × 505
= 5 × 5 × 101
⇒ The given number is a composite number.
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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