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
A number leaves remainder (4) when divided by (21), (28), and (36). Which is the smallest such number?HardLevel 13If the LCM of (2^a\times3^2\times5) and (2^3\times3^4\times5^2) is (2^5\times3^4\times5^2), which value of (a) is possible?HardLevel 13The HCF of two numbers is (12) and their product is (9504). What is their LCM?HardLevel 12If the HCF of (140) and (196) is (28), what will be their LCM?HardLevel 12Which option correctly gives the HCF of (2^3\times3^2\times7) and (2^5\times3\times7^2)?HardLevel 12If the prime factorisations of two numbers are (2^7\times3^2\times11) and (2^5\times3^4\times5), what will be their HCF?HardLevel 13What is the LCM of (63), (98), and (154)?HardLevel 13The product of two numbers is (66528) and their HCF is (72). What will be their LCM?HardLevel 13The HCF of two numbers is (48), their LCM is (1440), and one number is (240). What is the other number?HardLevel 13What is the smallest number exactly divisible by (54), (72), and (90)?HardLevel 13What is the greatest number that can exactly divide (225), (375), and (525)?HardLevel 13If (a=2^4\times3^2\times13) and (b=2^2\times3^5\times5\times13), what is (\frac{\text{LCM}}{\text{HCF}})?HardLevel 13Three machines give signals at intervals of (16), (24), and (40) minutes respectively. If they signal together now, after how many minutes will they signal together again?HardLevel 13If (x=2^a\times3^4\times5) and (y=2^6\times3^b\times11) have HCF (2^5\times3^3), which values are possible?HardLevel 13If (m=2^3\times3^a\times7) and (n=2^5\times3^2\times5^2\times7^b) have LCM (2^5\times3^4\times5^2\times7^3), which values are correct?HardLevel 13What is the smallest number that leaves remainder (9) when divided by (28), (42), and (56)?HardLevel 13A library has (168) mathematics books and (252) science books. They are to be kept in the maximum number of identical boxes so that each box has the same number of both types of books. How many boxes can be made?HardLevel 13If two numbers are coprime and their LCM is (667), what will be their product?HardLevel 13If (176=2^4\times11) and (264=2^3\times3\times11), what is the sum of their HCF and LCM?HardLevel 13If a number is divisible by both (2^5\times3^2\times7) and (2^3\times3^5\times11), what will be the power of (3) in the smallest such number?HardLevel 13