If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is
a. ab
b. a²b²
c. a³b²
d. a³b³

Solution:

It is given that,

p = ab² = a × b × b

q = a³b = a × a × a × b

Least Common Multiple(LCM) is a method to find the smallest common multiple between any two or more numbers

LCM is the product of the greatest power of each prime factor involved in the numbers.

LCM of p and q = LCM (ab², a³b) = a × b × b × a × a = a³b²

Therefore, LCM (p, q) is a³b²

✦ Try This: Find L.C.M. of 10 and 20

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

NCERT Exemplar Class 10 Maths Exercise 1.1 Problem 7

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is a. ab, b. a²b², c. a³ b², d. a³b³

Summary:

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is a³b²

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