Question

the L.c.m of 6x^2y, 9x^2yz,12x^2y^2z is
​

Answer 1

GCD of given algebraic expressions is 3x^{2}yz3x

2

yz .

Step-by-step explanation:

Gcd is Greatest Common Divisor, which means the greatest of all the common divisors of some numbers/expressions, which is actually just another name for Highest Common Factor (HCF).

Divisors are numbers/variables that exactly divide the number/expression.

So, we have to find the greatest common divisor of 6 x^{2} yz, \ 9x^{2}yz , \ 12x^{2}y^{2}z6x

2

yz, 9x

2

yz, 12x

2

y

2

z .

Divisors/Factors of 6 x^{2} yz6x

2

yz = 2 \times 3 \times x \times x \times y \times z=2×3×x×x×y×z

Divisors/Factors of 9 x^{2} yz = 3 \times 3 \times x \times x \times y \times z9x

2

yz=3×3×x×x×y×z

Divisors/Factors of 12 x^{2} y^{2} z = 3 \times 4 \times x \times x \times y \times y \times z12x

2

y

2

z=3×4×x×x×y×y×z

So, Common Divisors of all = 3 , x , x , y \ \& \ z3,x,x,y & z

Greatest Common Divisor of 6 x^{2} yz, \ 9x^{2}yz , \ 12x^{2}y^{2}z6x

2

yz, 9x

2

yz, 12x

2

y

2

z = 3 \times x \times x \times y \times z=3×x×x×y×z

= 3x^{2}yz=3x

2

yz

Thus, GCD of 6 x^{2} yz, \ 9x^{2}yz , \ 12x^{2}y^{2}z6x

2

yz, 9x

2

yz, 12x

2

y

2

z = 3x^{2}yz=3x

2

yz .

pls mark me brainliest.

thankyou