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 the HCF of two numbers is (24) and their LCM is (1080), which conclusion is correct?HardLevel 12If the HCF of two numbers is (24) and their LCM is (1080), which conclusion is correct?HardLevel 12If the HCF of two numbers is (20) and their LCM is (420), what is correct about their existence?HardLevel 12If (L) is the LCM of (2^2\times3^5\times5) and (2^4\times3^2\times5^3), what will be the power of (5) in (L)?HardLevel 12A number leaves remainder (0) when divided by (48), (80), and (112). What is the smallest such number?HardLevel 12If (H=2^3\times3^2) and (L=2^5\times3^4\times5) are respectively the HCF and LCM of two numbers, what is (\frac{L}{H})?HardLevel 12If the HCF of (252) and (378) is (126), what is their LCM?HardLevel 12If (p=2^4\times3^2) and (q=2^4\times3^2\times5), which statement about (p) and (q) is correct?HardLevel 12If (96), (128), and (160) are to be divided into the maximum equal parts, what will be the number of parts?HardLevel 12If the HCF of (2^3\times3\times5^2), (2^2\times3^4\times5), and (2^5\times3^2) is found, what will it be?HardLevel 12If the LCM of (35), (49), and (63) is found, what will be the power of (7) in it?HardLevel 12If two numbers are (18u) and (18v), where (u) and (v) are coprime and (uv=40), what will be their LCM?HardLevel 12If the HCF of (180) and (252) is (36), what is the value of (\frac{\text{LCM}}{\text{HCF}})?HardLevel 12Which number will surely be a multiple of both (2^4\times3^2) and (2^2\times3^3\times5)?HardLevel 12If (a=2^3\times5\times7) and (b=2^2\times3\times5\times7^2), which prime factors will appear in their HCF?HardLevel 12If (L) is the LCM and (H) is the HCF of (2^6\times3^2\times5) and (2^4\times3^5\times5^2), what will be the powers of (2) in (L) and (H) respectively?HardLevel 12If the LCM of two numbers is (2^5\times3^2\times7) and their HCF is (2^2\times3), what will be the power of (7) in their product?HardLevel 13If (L) is the LCM of (75), (125), and (200), what is the value of (L)?HardLevel 12If (L) is the LCM of (75), (125), and (200), what is the correct value of (L)?HardLevel 12A number leaves remainder (4) when divided by (21), (28), and (36). What is the smallest such number?HardLevel 12