Question

find the HCF of 15a*2b*3c*4,20a*3b*4c*5,25a*4b"5c*6​

Answer 1

Step-by-step explanation:

Solution

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The given monomials 10a

2

b

2

c

2

, 15ab

3

c

2

and 20b

3

c

2

can be factorised as follows:

10a

2

b

2

c

2

=2×5×a×a×b×b×c×c

15ab

3

c

2

=3×5×a×b×b×b×c×c

20b

3

c

2

=2×2×5×b×b×b×c×c

We know that HCF is the highest common factor, therefore, the HCF of 10a

2

b

2

c

2

, 15ab

3

c

2

and 20b

3

c

2

is:

HCF=5×b×b×c×c=5b

2

c

2

Also, the LCM is the least common multiple, therefore, the LCM of 10a

2

b

2

c

2

, 15ab

3

c

2

and 20b

3

c

2

is:

LCM=2×2×5×3×a×a×b×b×b×c×c=60a

2

b

3

c

2

Hence, the HCF is 5b

2

c

2

and LCM is 60a

2

b

3

c

2

.

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