Prime factorization, LCM, HCF

Concept: Prime Factorisation

Express each number as a product of its prime factors:

1. 140
2. 156
3. 3825
4. 5005
5. 7429

Concept: LCM & HCF by Prime Factorization

Find the LCM and HCF of the following pairs of integers and verify that LCM x HCF = product of the two numbers.

1. 26 and 91
2. 510 and 92
3. 336 and 54

Concept: LCM & HCF of 3 numbers by Prime Factorization

Find the LCM and HCF of the following integers by applying the prime factorisation method.

1. 12, 15 and 21
2. 17, 23 and 29
3. 8, 9 and 25

Concept: Product of 2 numbers = Product of LCM and HCF

Given that HCF (306, 657) = 9, find LCM (306, 657)

Concept: Prime factorization

Check whether 6ⁿ can end with the digit 0 for any natural number n.

Concept: Properties of Prime & Composite Numbers

Explain why 7 x 11 x 13 + 13 and 7 x 6 x 5 x 4 x 3 x 2 x 1 + 5 are composite numbers.

Concept: Word problem in LCM & HCF

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi take 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?