Find the $\text{l.c.m.}$ and $\text{g.c.d.}$ of the following by using the fundamental theorem of arithmetic: $84$,$90$,and $120$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) To find the $\text{l.c.m.}$ and $\text{g.c.d.}$ using the fundamental theorem of arithmetic,we first find the prime factorization of each number:
$84 = 2^2 \times 3^1 \times 7^1$
$90 = 2^1 \times 3^2 \times 5^1$
$120 = 2^3 \times 3^1 \times 5^1$
$\text{g.c.d.}$ is the product of the smallest power of each common prime factor:
$\text{g.c.d.}(84, 90, 120) = 2^1 \times 3^1 = 6$
$\text{l.c.m.}$ is the product of the highest power of each prime factor present in the numbers:
$\text{l.c.m.}(84, 90, 120) = 2^3 \times 3^2 \times 5^1 \times 7^1 = 8 \times 9 \times 5 \times 7 = 2520$

Explore More

Similar Questions

Prove that any positive odd integer is of the form $6m+1$ or $6m+3$ or $6m+5$,where $m \in N \cup \{0\}$.

Using Euclid's division algorithm,find the Highest Common Factor $(HCF)$ of the following pair of numbers and determine if they are co-prime:
$847, 2160$

By using the fact $g.c.d. (a, b) \times l.c.m. (a, b) = a \times b$,find $l.c.m. (26, 91)$.

Simplify: $\frac{\sqrt{4-\sqrt{7}}}{\sqrt{8+3 \sqrt{7}-2 \sqrt{2}}}$

Difficult
View Solution

Prove that $\frac{1}{\sqrt{2}}$ is an irrational number.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo