Mathematics
HCF and LCM using prime factorisation
अभाज्य गुणनखंडन द्वारा महत्तम समापवर्तक और लघुत्तम समापवर्त्य
In this Class 10 Mathematics topic from Real Numbers, students learn to find the HCF and LCM of two or more numbers through prime factorisation. They break each number into prime factors, compare the resulting powers, and select the appropriate common factors: the lowest powers for HCF and the highest powers for LCM. The topic also develops accuracy in writing factor trees, simplifies comparison between methods, and helps students apply these concepts to numerical and everyday problem-solving situations.
Practice questions
If two numbers have HCF (24) and LCM (720), which of the following pairs can be possible?HardLevel 10What is the greatest number that leaves remainder (5) when dividing (137), (185), and (257)?HardLevel 10Three bells ring at intervals of (18), (24), and (30) minutes. If they start ringing together, after how many minutes will they ring together again?HardLevel 10A shopkeeper wants to pack (96), (144), and (240) sweets equally into boxes. What is the greatest number of sweets that can be put in each box?HardLevel 10Two numbers are (a=2^5\times 3^2\times 5) and (b=2^3\times 3^4\times 5^2). What is the value of (\frac{\text{LCM}}{\text{HCF}})?HardLevel 10If (x=2^4\times 3^3\times 7) and (y=2^2\times 3^5\times 5), what is (\frac{xy}{\text{HCF}}) equal to?HardLevel 10If the HCF of two numbers is (1) and their product is (7429), what is their LCM?HardLevel 10The HCF of two numbers is (2^2\times 3^2) and their LCM is (2^5\times 3^2\times 5\times 7). If one number is (2^5\times 3^2\times 5), what is the other number?HardLevel 10What is the smallest number greater than (1000) that is exactly divisible by (36), (48), and (60)?HardLevel 10If (A=2^6\times 3^2\times 5) and (B=2^4\times 3^5\times 7), how many prime factors are there in their HCF, counting repetition?HardLevel 10If (A=2^3\times 3^2\times 11) and (B=2^5\times 3\times 5\times 11^2), how many distinct prime factors are there in their LCM?HardLevel 10Two numbers are (2^a\times 3^2\times 5) and (2^4\times 3^b\times 7). If their HCF is (2^3\times 3^2), which option is correct for ((a,b))?HardLevel 10Two numbers are (2^a\times 3\times 5^2) and (2^2\times 3^4\times 5^b). If their LCM is (2^5\times 3^4\times 5^3), what is ((a,b))?HardLevel 10If (72), (108), and (180) are divided by the greatest possible number and each division is exact, what is that number?HardLevel 10What is the smallest number which leaves remainder (0) when divided by (45), (54), and (72)?HardLevel 10The HCF of two numbers is (15) and their LCM is (630). Which statement is definitely true?HardLevel 10If the prime factorisations of two numbers are (2^3\times3^2\times5) and (2^2\times3^3\times7), what is their HCF?HardLevel 10If the HCF of two numbers is (18), their LCM is (540), and one number is (90), what is the other number?HardLevel 10The prime factorisations of three numbers are (2^4\times3\times5^2), (2^2\times3^3\times5), and (2^3\times3^2\times7). What is their LCM?HardLevel 10The product of two numbers is (12960) and their HCF is (36). What is their LCM?HardLevel 10