(B) First,find the $HCF$ of $65$ and $117$ using prime factorization:$65 = 5 \times 13$$117 = 9 \times 13 = 3^2 \times 13$Therefore,$HCF(65, 117) = 13

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(B) First,find the $HCF$ of $65$ and $117$ using prime factorization:$65 = 5 \times 13$$117 = 9 \times 13 = 3^2 \times 13$Therefore,$HCF(65, 117) = 13$.Given the equation: $65m - 117 = HCF(65, 117)$.Substitute the $HCF$ value: $65m - 117 = 13$.Add $117$ to both sides: $65m = 13 + 117$.$65m = 130$.Divide by $65$: $m = 130 / 65$.$m = 2$.

Class 10 Mathematics Real Numbers HCF and LCM by Prime Factorisation

Medium

If $HCF(65, 117) = 65m - 117$,then find the value of $m$.

A
$1$
B
$2$
C
$3$
D
$4$

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HCF and LCM by Prime Factorisation

If $p$ and $q$ are distinct prime integers,then their Least Common Multiple $(LCM)$ is . . . . . . .

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Find the $LCM(26, 91)$.

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If the greatest common divisor (g.c.d.) of $a$ and $b$ is $d$,then which of the following statements is false?

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For two positive integers $a$ and $b$,if $\text{HCF}(a, b) = 7$ and $\text{LCM}(a, b) = 385$,then which of the following is true?

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If the $HCF(a, b) = 16$, then which of the following cannot be the $LCM(a, b)$? (Options: $32, 72, 64$)

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If $HCF(65, 117) = 65m - 117$,then find the value of $m$.

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If $p$ and $q$ are distinct prime integers,then their Least Common Multiple $(LCM)$ is . . . . . . .

Find the $LCM(26, 91)$.

If the greatest common divisor (g.c.d.) of $a$ and $b$ is $d$,then which of the following statements is false?

For two positive integers $a$ and $b$,if $\text{HCF}(a, b) = 7$ and $\text{LCM}(a, b) = 385$,then which of the following is true?

If the $HCF(a, b) = 16$, then which of the following cannot be the $LCM(a, b)$? (Options: $32, 72, 64$)

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