Question

find the hcf and lcm of 24 , 60 , 150 by prime factorisation method​

Answer 1

Step-by-step explanation:

BY PRIME FACTORISATION METHOD WE HAVE :-

2|24| 2|60| 2|150|

2|12| 2|30| 3|75|

2|6| 3|15| 5|25|

3|3| 5|5| 5|5|

_______________________________

24=2×2×2×3

60=2×2×3×5

150=2×3×5×5

HCF:- 2×3=6

LCM:- 2×2×2×3×5×5=600

RULES TO KEEP IN MIND :-

• TO FIND HCF WE TAKE THE NUMBERS WHICH ARE COMMON IN THE GIVEN NO. AND HAVE LEAST POWER.
• SIMILARLY TO FIND LCM WE NEED TO TAKE THE COMMON NUMBERS WITH LESS POWER.

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The HCF is 6 and LCM is 600

$\textbf{\underline{\underline{Explanation :-}}}$

HCF of 24 , 60 and 150 :-

$\textsf{Prime Factorization of 24 :}$

$\begin{array}{r|l} 2 & 24 \\\cline{1-2} 2 & 12 \\\cline{1-2} 2 & 6 \\ \cline{1-2} 2 & 3 \\\cline{1-2} 3 & 3 \\\cline{1-2} & 1 \end{array}$

$\textsf{Prime Factorization of 60 :}$

$\begin{array}{r|l} 2 & 60 \\\cline{1-2} 2 & 30 \\\cline{1-2} 3 & 15 \\ \cline{1-2} 5 & 5 \\\cline{1-2} & 1 \end{array}$

$\textsf{Prime Factorization of 150 :}$

$\begin{array}{r|l} 2 & 150 \\\cline{1-2} 3 & 75 \\\cline{1-2} 5 & 25 \\ \cline{1-2} 5 & 5 \\\cline{1-2} & 1 \end{array}$

24 = 2 × 2 × 2 × 3

60 = 2 × 2 × 3 × 5

150 = 2 × 3 × 5 × 5

HCF = 2 × 3 = 6

$\boxed{\boxed{\sf{HCF=6}}}$

$\rule{300}{1}$

LCM of 24 , 60 and 150 :-

$\begin{array}{r|l} 2 & 24,60,150 \\\cline{1-2} 2 & 12,30,75 \\\cline{1-2} 2 & 6,15,75 \\ \cline{1-2} 3 & 3,15,75 \\\cline{1-2} 5 & 1,5,25 \\\cline{1-2} 5 & 1,1,5 \\\cline{1-2} & 1,1,1 \end{array}$

LCM = 2 × 2 × 2 × 3 × 5 × 5

$\implies$ 600

$\boxed{\boxed{\sf{LCM=600}}}$

$\therefore$ The HCF is 6 and LCM is 600