Question

Find the l.c.m and h.c.f 45,60,75 prime foctoraisation explnai it?

Answer 1

Question :

Find the LCM and HCF of 45,60, 75 by prime factorization method.

Answer :

HCF ( 45,60 and 75 ) = 15.

LCM ( 45,60 and 75 ) = 900.

Step-by-step explanation:

we have Given no.

$\\ \: \: \tt1) \: 45.$

$</p><p></p><p>\begin{array}{r | l}</p><p></p><p>5 & 45 \\</p><p></p><p>\cline{2-2} 3 & 9 \\</p><p></p><p>\cline{2-2} 3 & 3 \\</p><p></p><p>\cline{2-2} & 1 </p><p></p><p>\end{array}$

$\\ \\ \: \: \tt2)60.$

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

$\: \: \tt 3)75.$

$</p><p></p><p>\begin{array}{r | l}</p><p></p><p>5 & 75 \\</p><p></p><p>\cline{2-2} 3 & 15 \\</p><p></p><p>\cline{2-2} 5 & 5 \\</p><p></p><p>\cline{2-2} & 1 </p><p></p><p>\end{array}$

$\\ \: \: \tt There \: product \: be \: \\ \\ \: \: \: \: \: \: 45 \longrightarrow \: 3 \times 3 \times 5. \\ \\ \: \: \: \: \: \: \tt60 \longrightarrow 2 \times 2 \times 3 \times 5. \\ \\ \: \: \: \: \: \: 75 \longrightarrow 3 \times 5 \times 5. \\ \\ \\ \: \: \tt HCF = 15. \\ \\ \: \: \tt LCM = 900.$

Therefore,the value of LCM be 900. and HCF be 15.

Some information :

LCM stand for Least Common multiple.

HCF stand for Highest Common factor.

Answer 2

♦Answer:-

→45=5×3×3

→60=2×2×5×3

→75=5×3×5

★For Prime Factorization refer Attachment★

→HCF(45,60 & 75)=3×5=15

→LCM(45,60 & 75)=5×3×3×2×2×5=900

$\rule{200}{1}$

$\orange{\boxed{\blue{\underline{\green{\mathrm{HCF:-}}}}}}$

→HCF(HIGHEST COMMON FACTOR) is the highest Factor and common factor of two or more numbers.

$\rule{200}{1}$

$\red{\boxed{\purple{\underline{\orange{\mathrm{LCM:-}}}}}}$

→LCM(LEAST COMMON MULTIPLE) is the lowest/least common multiple of two or more numbers and is the smallest number by which the numbers can be divided.

$\rule{200}{8}$